llm5_word_list.txt

bayesian	('analysis', 'estimate', 'analog', 'procedure', 'analysis', 'featured', 'inference', 'featured', 'filtering', 'analysis', 'analysis', 'analysis', 'estimator', 'analysis', 'treat', 'proportion')
analysis	('bayesian', 'statistical', 'bayesian', 'somewhat', 'bayesian', 'bayesian', 'bayesian', 'maximum', 'error', 'error', 'error', 'absolute', 'error', 'fixed', 'error', 'confidence', 'error', 'confidence', 'error', 'absolute', 'error', 'chebyshev', 'error', 'absolute', 'error', 'absolute', 'error', 'error', 'error', 'confidence', 'error', 'remez', 'error', 'absolute', 'error', 'absolute', 'error', 'absolute', 'error', 'accuracy', 'error', 'accuracy', 'bayesian', 'likelihood', 'likelihood', 'cluster', 'technique', 'cluster', 'math', 'cluster', 'find', 'overlapping', 'cluster', 'multivariate', 'cluster', 'series', 'conditional', 'multivariate', 'multivariate', 'critical', 'one', 'series', 'expectation', 'series', 'point', 'series', 'hawkes', 'series', 'hawkes', 'series', 'hawkes', 'series', 'conditional', 'series', 'conditional', 'series', 'point', 'series', 'marked', 'series', 'marked', 'series', 'mark', 'series', 'marked', 'detailed', 'stigler', 'series', 'marked', 'percentage', 'series', 'multidimensional', 'series', 'marked', 'series', 'marked', 'series', 'marked', 'series', 'marked', 'series', 'bond', 'series', 'hawkes', 'imbue', 'multivariate', 'nonlinear', 'variance', 'mean', 'group', 'manova', 'procedure', 'series', 'moving', 'series', 'cumulative', 'series', 'series', 'series', 'deterministic', 'series', 'series', 'predictability', 'series', 'moving', 'series', 'series', 'moving', 'series', 'graph', 'series', 'moving', 'series', 'moving', 'data', 'series', 'process', 'heartbeat', 'series', 'time', 'series', 'anova', 'series', 'covariance', 'series', 'wiener', 'series', 'uncorrelated', 'population', 'evans', 'gauss', 'astronomical', 'data')
statistical	('analysis', 'procedure', 'common', 'analyses', 'table', 'tests', 'frequency', 'peak', 'quartile', 'median', 'test', 'size', 'side', 'plus', 'find', 'quartile', 'median', 'order', 'median', 'mean', 'skewness', 'median', 'outlier', 'based', 'mean', 'phenomenon', 'various', 'deviation', 'dispersion', 'smallest', 'data', 'depth', 'descriptive', 'rank', 'average', 'dispersion', 'median', 'distribution', 'distribution', 'order', 'median', 'skewness', 'median', 'kenney', 'range', 'range', 'median', 'tails', 'skewness', 'distribution', 'proportional', 'series', 'rank', 'deviation', 'dispersion', 'cumulant', 'example', 'based', 'mean', 'morrison', 'quantity', 'matrix', 'correlation', 'set', 'set', 'several', 'quantities', 'standard', 'point', 'mean', 'deviation', 'median', 'function', 'process', 'error', 'correlation', 'distribution', 'distribution', 'method', 'test', 'estimation', 'method', 'estimation', 'order', 'midrange', 'minimum', 'median', 'difference', 'regression', 'rank', 'test', 'work', 'domain', 'range', 'subjectively', 'procedure', 'inequality', 'distribution', 'paradox', 'trend', 'extant', 'problem', 'distribution', 'distribution', 'power', 'power', 'test', 'underlying', 'number', 'distribution', 'quantity', 'through', 'object', 'find', 'median', 'triangle', 'median', 'use', 'test', 'coefficient', 'rank', 'rank', 'test', 'decreasing', 'rank', 'rank', 'hinge', 'mean', 'median', 'plot', 'correlation', 'anticorrelated', 'correlation', 'series', 'asymptotic', 'expansion', 'asymptotic', 'theorem', 'asymptotic', 'series', 'asymptotic', 'theorem', 'asymptotic', 'index', 'indices', 'index', 'indices', 'index', 'indices', 'index', 'indices', 'number', 'indices', 'index', 'indices', 'index', 'indices', 'index', 'indices', 'index', 'indices', 'index', 'indices', 'chart', 'plot', 'draw', 'plot', 'quartile', 'median', 'face', 'polygon', 'plot', 'plot', 'curve', 'histogram', 'simple', 'hinge', 'display', 'plot', 'ogive', 'plot', 'chart', 'plot', 'plot', 'plotting', 'diagram', 'stemleafplot', 'plot', 'value', 'hypothesis', 'variance', 'darling', 'anova', 'anova', 'bessel', 'formula', 'formula', 'independent', 'correction', 'testing', 'test', 'test', 'problem', 'test', 'test', 'test', 'hypothesis', 'important', 'hypotheses', 'hypothesis', 'testing', 'test', 'test', 'test', 'test', 'test', 'kuiper', 'ratio', 'procedure', 'manova', 'ratio', 'hypothesis', 'lemma', 'hypothesis', 'hypothesis', 'test', 'test', 'comparison', 'value', 'specificity', 'power', 'power', 'test', 'plot', 'probability', 'sensitivity', 'specificity', 'test', 'significance', 'test', 'test', 'test', 'significance', 'test', 'value', 'probability', 'specificity', 'sensitivity', 'test', 'hypothesis', 'hypothesis', 'positive', 'power', 'power', 'specificity', 'test', 'test', 'probability', 'test', 'correction', 'several', 'comparison', 'test', 'test', 'error', 'error', 'specificity', 'test', 'error', 'error', 'specificity', 'test', 'score', 'particular', 'quantities', 'implementation', 'type', 'maximum', 'distribution', 'snedecor', 'distribution', 'continuous', 'distribution', 'type', 'other', 'distribution', 'equilibrium', 'bessel', 'formula', 'probability', 'distribution', 'device', 'different', 'quantity', 'range', 'range', 'over', 'range', 'case', 'distribution', 'function', 'distribution', 'mimic', 'properties', 'moment')
procedure	('statistical', 'endeavors', 'bayesian', 'method', 'finding', 'above', 'repeated', 'above', 'identities', 'nonparametric', 'observation', 'involves', 'statistical', 'endeavors', 'folding', 'only', 'mathematical', 'finding', 'approach', 'function', 'minimize', 'line', 'results', 'applying', 'solution', 'converge', 'above', 'undertaken', 'specific', 'likelihood', 'statistical', 'analysis', 'testing', 'likelihood', 'likelihood', 'manova', 'time', 'repeated')
endeavors	('procedure', 'estimate', 'procedure', 'estimate')
estimate	('endeavors', 'parameters', 'bayesian', 'unbiased', 'normal', 'unbiased', 'quantile', 'variance', 'kenney', 'educated', 'important', 'accurate', 'possible', 'possible', 'uncertainty', 'uncertainty', 'determined', 'calculate', 'based', 'estimator', 'error', 'error', 'confidence', 'based', 'error', 'estimator', 'l', 'estimator', 'r', 'r', 'arguments', 'l', 'r', 'r', 'likelihood', 'parameter', 'r', 'l', 'm', 'l', 'rank', 'l', 'm', 'l', 'r', 'r', 'size', 'population', 'standard', 'error', 'square', 'order', 'population', 'efron', 'observation', 'joint', 'ryan', 'sample', 'endeavors', 'code', 'r', 'spearman', 'l', 'mean', 'regression', 'most', 'most', 'linearized', 'theorem', 'probability', 'correction', 'fisher', 'r', 'order', 'properties')
parameters	('estimate', 'underlying', 'likelihoods', 'results')
underlying	('parameters', 'distribution', 'distribution', 'central', 'mean', 'conjectured', 'distribution', 'common', 'distribution', 'distribution', 'distribution', 'nature', 'parameter', 'distribution', 'matching', 'statistical', 'reproduces', 'assumption', 'distribution', 'complexity', 'system', 'properties', 'parent', 'properties', 'properties')
distribution	('underlying', 'based', 'begin', 'based', 'over', 'prior', 'collect', 'calculate', 'observed', 'function', 'normalize', 'mode', 'parameter', 'cannot', 'prior', 'uniform', 'uniform', 'absolute', 'frequency', 'relative', 'probability', 'over', 'probability', 'logarithmic', 'above', 'hill', 'below', 'first', 'table', 'first', 'logarithmic', 'refers', 'refers', 'two', 'bimodal', 'mode', 'two', 'bimodal', 'descriptive', 'unimodal', 'kenney', 'frequency', 'multiperfect', 'table', 'frequency', 'independent', 'total', 'frequency', 'relative', 'probability', 'continuous', 'frequency', 'data', 'frequency', 'descriptive', 'frequency', 'frequency', 'histogram', 'single', 'cumulative', 'function', 'zero', 'two', 'single', 'unimodal', 'one', 'pattern', 'moore', 'determined', 'similar', 'plotting', 'wolfram', 'empirical', 'plotting', 'divided', 'frequency', 'relative', 'relative', 'frequency', 'relative', 'proportion', 'statistical', 'statistical', 'equal', 'uniform', 'range', 'probability', 'statistical', 'vector', 'refers', 'refers', 'single', 'unimodal', 'unimodal', 'zipf', 'probability', 'normal', 'fall', 'normal', 'normal', 'p', 'inverse', 'moment', 'denotes', 'normal', 'polykay', 'likelihood', 'maximum', 'maximum', 'maximum', 'observation', 'unbiased', 'taken', 'underlying', 'variance', 'standard', 'sum', 'conditional', 'conditional', 'only', 'probability', 'governed', 'probability', 'zero', 'normal', 'uniquely', 'normal', 'correlation', 'excess', 'excess', 'different', 'same', 'several', 'theoretical', 'denotes', 'equal', 'encountered', 'tail', 'normal', 'correspondence', 'fact', 'perfectly', 'degree', 'high', 'mean', 'discrete', 'mean', 'consisting', 'incomplete', 'chi-squared', 'exponential', 'gamma', 'gumbel', 'half-normal', 'laplace', 'logistic', 'log', 'maxwell', 'normal', 'pareto', 'rayleigh', 'triangular', 'uniform', 'following', 'binomial', 'discrete', 'geometric', 'poisson', 'zipf', 'mean', 'zero', 'uniquely', 'th', 'measured', 'equal', 'measured', 'mean', 'probability', 'continuous', 'population', 'mean', 'wolfram', 'discrete', 'root-mean-square', 'continuous', 'variance', 'variance', 'using', 'third', 'excess', 'computed', 'underlying', 'pearson', 'gamma', 'variance', 'mean', 'sample', 'sample', 'deviation', 'variance', 'ungrouped', 'th', 'grouped', 'class', 'left', 'pronounced', 'function', 'skewness', 'th', 'beta', 'binomial', 'chi-squared', 'exponential', 'extreme', 'geometric', 'half-normal', 'hypergeometric', 'laplace', 'log', 'maxwell', 'negative', 'normal', 'poisson', 'rayleigh', 'several', 'probability', 'square', 'slightly', 'deviation', 'finite', 'underlying', 'normal', 'root', 'deviation', 'sample', 'variance', 'standard', 'normal', 'gamma', 'deviation', 'variance', 'standard', 'many', 'standard', 'variate', 'population', 'possible', 'variance', 'maxwell', 'rayleigh', 'underlying', 'underlying', 'sample', 'model', 'set', 'variance', 'sigma', 'bivariate', 'bivariate', 'normal', 'multivariate', 'normal', 'statistical', 'statistical', 'probability', 'normal', 'normal', 'complete', 'normal', 'quadrant', 'normal', 'continuous', 'box', 'normal', 'multivariate', 'normal', 'normal', 'normal', 'price', 'normal', 'distributed', 'variable', 'immigrant', 'multinormal', 'continuous', 'multivariate', 'normal', 'binomial', 'multivariable', 'multivariate', 'multivariate', 'normal', 'multivariate', 'normal', 'multinormal', 'generalization', 'normal', 'mean', 'normal', 'solution', 'normal', 'continuous', 'bivariate', 'normal', 'gaussian', 'normal', 'trivariate', 'normal', 'three', 'normal', 'unit', 'normal', 'continuous', 'bivariate', 'normal', 'multivariate', 'normal', 'normal', 'normal', 'mean', 'wishart', 'scale', 'wishart', 'most', 'wishart', 'wishart', 'continuous', 'f', 'f', 'multivariate', 'binomial', 'hotelling', 't2', 'sample', 'almost', 'function', 'value', 'hinge', 'association', 'data', 'ignored', 'birthdays', 'event', 'coin', 'tosses', 'bernoulli', 'bernoulli', 'range', 'function', 'function', 'depend', 'probability', 'function', 'joint', 'function', 'function', 'simplifies', 'latter', 'probability', 'function', 'probability', 'common', 'underlying', 'based', 'properly', 'probability', 'continuous', 'sum', 'discrete', 'cumulative', 'axiom', 'function', 'statistical', 'uniform', 'continuous', 'derivative', 'cumulative', 'probability', 'function', 'difference', 'probability', 'probability', 'moment', 'gamma', 'continuous', 'cornish', 'difference', 'discrete', 'discrete', 'discrete', 'function', 'joint', 'function', 'product', 'ratio', 'ratio', 'sum', 'sum', 'range', 'probability', 'subset', 'bit', 'nature', 'domain', 'continuous', 'discrete', 'discrete', 'discrete', 'function', 'probability', 'number', 'saint', 'geometric', 'martingale', 'depend', 'statistical', 'statistical', 'two-dimensional', 'uniformly', 'bivariate', 'normal', 'normal', 'normal', 'uniform', 'theory', 'uniformly', 'small', 'concentration', 'disappears', 'uniform', 'number', 'very', 'logit', 'uniformity', 'uniform', 'theory', 'uniform', 'theory', 'random', 'random', 'general', 'random', 'statistical', 'random', 'expected', 'uniformly', 'taken', 'satisfying', 'properties', 'specified', 'selection', 'almost', 'other', 'course', 'impossible', 'differential', 'uniform', 'uniform', 'sphere', 'power-law', 'uniform', 'uniform', 'normalization', 'uniform', 'random', 'random', 'uniform', 'uniform', 'theory', 'uniform', 'theory', 'uniform', 'uniform', 'investigation', 'above', 'borel-tanner', 'trott', 'borel-tanner', 'complex', 'tanner', 'continuous', 'normal', 'random', 'levy', 'levy', 'deviation', 'moment', 'examine', 'binomial', 'catalan', 'tail', 'pelya', 'equally', 'normal', 'correlation', 'normal', 'correlation', 'coefficient', 'plugging', 'skew', 'variable', 'normal', 'regression', 'assumption', 'hypergeometric', 'permutation', 'permutation', 'derivative', 'need', 'normal', 'similarly', 'bernoulli', 'binomial', 'normal', 'weak', 'approximated', 'approximated', 'standardized', 'normal', 'derivative', 'function', 'poisson', 'frequency', 'frequency', 'frequency', 'continuous', 'continuous', 'number', 'frequency', 'frequency', 'bin', 'frequency', 'frequency', 'anderson', 'number', 'classes', 'observed', 'limiting', 'chi-squared', 'kenney', 'probability', 'assumes', 'squared', 'significance', 'different', 'normal', 't2', 'test', 'true', 'most', 'find', 'hypothesis', 'expected', 'normal', 'r', 'underlying', 'observed', 'probability', 'dependent', 'bernoulli', 'coin', 'process', 're', 'relative', 'gamma', 'beta', 'two', 'beta', 'prior', 'binomial', 'function', 'beta', 'wolfram', 'beta', 'normalized', 'beta', 'continuous', 'gamma', 'gamma', 'probability', 'prime', 'continuous', 'binormal', 'continuous', 'bivariate', 'normal', 'study', 'einstein', 'continuous', 'einstein', 'dirac', 'sigmoid', 'lorentzian', 'lorentzian', 'lorentz', 'continuous', 'continuous', 'describing', 'behavior', 'horizontal', 'above', 'cauchy', 'cumulative', 'cumulative', 'written', 'cauchy', 'wolfram', 'moment', 'undefined', 'cauchy', 'cauchy', 'statistical', 'cauchy', 'cauchy', 'seen', 'cauchy', 'continuous', 'normal', 'normal', 'chi', 'freedom', 'followed', 'variable', 'half-normal', 'rayleigh', 'chi', 'chi', 'wolfram', 'function', 'function', 'regularized', 'chi', 'continuous', 'chi', 'squared', 'half', 'normal', 'rayleigh', 'rayleigh', 'freedom', 'gamma', 'number', 'distributed', 'function', 'cumulative', 'function', 'chi-squared', 'wolfram', 'moment', 'function', 'mean', 'general', 'noncentral', 'chi', 'squared', 'continuous', 'chi', 'chi', 'inverse', 'squared', 'noncentral', 'squared', 'normal', 'normal', 'snedecor', 'statistical', 'approximate', 'continuous', 'variate', 'continuity', 'binomial', 'binomial', 'normal', 'normal', 'continuous', 'continuous', 'continuous', 'beta', 'beta', 'bivariate', 'bivariate', 'cauchy', 'cauchy', 'chi', 'chi', 'chi', 'squared', 'correlation', 'discrete', 'exponential', 'exponential', 'extreme', 'value', 'f', 'f', 'fermi', 'dirac', 'fisher', 'gamma', 'half', 'normal', 'laplace', 'laplace', 'lattice', 'lattice', 'levy', 'levy', 'logarithmic', 'logarithmic', 'log', 'series', 'logistic', 'logistic', 'maxwell', 'maxwell', 'normal', 'normal', 'pareto', 'pareto', 'pearson', 'iii', 'poisson', 'poisson', 'ratio', 'ratio', 'rayleigh', 'rayleigh', 'rice', 'rice', 'snedecor', 'uniform', 'weibull', 'weibull', 'univariate', 'multivariate', 'sklar', 'bivariate', 'normal', 'correlation', 'excess', 'difference', 'rate', 'change', 'integer', 'erlang', 'probability', 'necessarily', 'evans', 'p', 'using', 'erlang', 'continuous', 'exponential', 'exponential', 'gamma', 'gamma', 'poisson', 'poisson', 'error', 'continuous', 'normal', 'normal', 'function', 'continuous', 'normal', 'normal', 'rate', 'change', 'waiting', 'probability', 'function', 'exponential', 'only', 'continuous', 'geometric', 'properly', 'exponential', 'continuous', 'extreme', 'value', 'geometric', 'geometric', 'poisson', 'poisson', 'most', 'gumbel', 'extreme', 'statistic', 'fisher-tippett', 'maximum', 'value', 'value', 'maximum', 'location', 'function', 'normalized', 'satisfies', 'extreme', 'gumbel-type', 'gumbel-type', 'weibull-type', 'weibull', 'two-parameter', 'weibull', 'value', 'continuous', 'euler', 'gumbel', 'order', 'weibull', 'statistical', 'testing', 'statistic', 'cumulative', 'function', 'first', 'smaller', 'f', 'continuous', 'beta', 't2', 'noncentral', 'f', 'regularized', 'f', 'f', 'f', 'normal', 'normal', 'variance', 'study', 'dirac', 'continuous', 'bose', 'einstein', 'einstein', 'tippett', 'continuous', 'extreme', 'value', 'gumbel', 'gumbel', 'general', 'kenney', 'z', 'continuous', 'beta', 'beta', 'beta', 'prime', 'chi', 'squared', 'gamma', 'gamma', 'normal', 'normal', 'student', 'gamma', 'general', 'beta', 'naturally', 'two', 'above', 'rate', 'integer', 'special', 'probability', 'gamma', 'function', 'describing', 'fourier', 'moment', 'using', 'gamma', 'closely', 'independent', 'gamma', 'gamma', 'variate', 'sum', 'gamma', 'ratio', 'ratio', 'beta', 'gamma', 'ratio', 'beta', 'gamma', 'gamma', 'continuous', 'beta', 'beta', 'chi', 'squared', 'erlang', 'erlang', 'difference', 'continuous', 'normal', 'difference', 'gaussian', 'continuous', 'normal', 'normal', 'product', 'continuous', 'normal', 'product', 'ratio', 'continuous', 'normal', 'ratio', 'sum', 'continuous', 'normal', 'sum', 'gibrat', 'continuous', 'over', 'normal', 'function', 'gibrat', 'continuous', 'log', 'normal', 'most', 'gumbel', 'extreme', 'statistic', 'term', 'minimum', 'value', 'value', 'minimum', 'gumbel', 'location', 'function', 'constant', 'taken', 'over', 'function', 'function', 'cumulative', 'cumulative', 'normal', 'normal', 'probability', 'gumbel', 'continuous', 'extreme', 'value', 'inverse', 'gumbel', 'half-normal', 'normal', 'probability', 'normal', 'continuous', 'normal', 'normal', 'univariate', 'proportional', 'unit', 'hotelling', 'denoted', 'sample', 'hotelling', 'continuous', 'f', 'f', 'hotelling', 'wishart', 'wald', 'wald', 'over', 'function', 'gaussian', 'wolfram', 'gaussian', 'continuous', 'normal', 'normal', 'double', 'exponential', 'abramowitz', 'cumulative', 'laplace', 'continuous', 'levy', 'infinite', 'normal', 'levy', 'levy', 'wolfram', 'levy', 'continuous', 'cauchy', 'cauchy', 'levy', 'normal', 'general', 'log', 'normal', 'normal', 'results', 'results', 'cumulative', 'normal', 'sigma', 'size', 'normal', 'continuous', 'log', 'series', 'logarithmic', 'logarithmic', 'weibull', 'weibull', 'logarithmic', 'continuous', 'variate', 'function', 'function', 'logarithmic', 'logarithmic', 'arising', 'raw', 'logarithmic', 'continuous', 'benford', 'normal', 'log', 'series', 'continuous', 'probability', 'p', 'equation', 'logistic', 'wolfram', 'logistic', 'continuous', 'logistic', 'lorentz', 'continuous', 'cauchy', 'cauchy', 'lorentzian', 'continuous', 'cauchy', 'cauchy', 'map-airy', 'statistical', 'probability', 'function', 'airy', 'continuous', 'airy', 'maxwell-boltzmann', 'maxwell-boltzmann', 'speeds', 'over', 'maxwell', 'continuous', 'exponential', 'exponential', 'normal', 'normal', 'rayleigh', 'rayleigh', 'chi-squared', 'noncentrality', 'squared', 'continuous', 'chi', 'squared', 'noncentral', 'two', 'probability', 'noncentral', 'f', 'continuous', 'f', 'f', 'kind', 'wolfram', 'student', 'continuous', 'student', 'amazingly', 'difference', 'mean', 'difference', 'continuous', 'normal', 'normal', 'normal', 'ratio', 'normal', 'sum', 'normal', 'statistic', 'probability', 'physicists', 'gaussian', 'because', 'normal', 'approximation', 'subsequently', 'normal', 'wolfram', 'general', 'arbitrary', 'normal', 'converted', 'changing', 'different', 'normal', 'normal', 'limiting', 'sample', 'variance', 'properly', 'cumulative', 'many', 'assumed', 'variate', 'finite', 'many', 'members', 'situations', 'normal', 'normal', 'normal', 'respectively', 'arbitrary', 'cauchy', 'using', 'normal', 'characteristic', 'normal', 'moment-generating', 'normal', 'normal', 'general', 'simplifies', 'normal', 'kenney', 'normal', 'generated', 'via', 'normal', 'use', 'normal', 'solution', 'named', 'normal', 'special', 'making', 'gamma', 'normal', 'normal', 'continuous', 'binomial', 'binomial', 'bivariate', 'normal', 'box', 'function', 'fisher', 'normal', 'inverse', 'gaussian', 'kolmogorov', 'normal', 'function', 'product', 'normal', 'ratio', 'normal', 'sum', 'owen', 'ratio', 'standard', 'normal', 'tetrachoric', 'function', 'normal', 'function', 'normal', 'function', 'berry', 'normal', 'owen', 'product', 'kind', 'plotted', 'product', 'continuous', 'normal', 'difference', 'normal', 'normal', 'normal', 'ratio', 'normal', 'sum', 'seen', 'ratio', 'ratio', 'cauchy', 'direct', 'ratio', 'continuous', 'cauchy', 'cauchy', 'normal', 'difference', 'normal', 'normal', 'normal', 'product', 'normal', 'sum', 'amazingly', 'sum', 'normal', 'mean', 'new', 'sum', 'continuous', 'cramer', 'difference', 'normal', 'normal', 'normal', 'product', 'normal', 'ratio', 'probability', 'function', 'function', 'pareto', 'continuous', 'solution', 'solution', 'case', 'skewed', 'similar', 'abramowitz', 'characteristic', 'iii', 'continuous', 'pearson', 'iv', 'covariance', 'normal', 'normal', 'inverse', 'normal', 'significance', 'normal', 'probability', 'function', 'rayleigh', 'continuous', 'maxwell', 'maxwell', 'rice', 'rice', 'continuous', 'rayleigh', 'rayleigh', 'term', 'free', 'capable', 'well', 'special', 'case', 'savageau', 'continuous', 'beyer', 'f', 'continuous', 'beta', 'beta', 'chi', 'squared', 'student', 'normal', 'normal', 'zero', 'function', 'oeis', 'normal', 'continuous', 'erf', 'normal', 'normal', 'normal', 'function', 'published', 'student', 'random', 'studenttdistribution', 'student', 'cumulative', 'value', 'multivariatestatistics`', 'useful', 'same', 'student', 'continuous', 'bessel', 'cumulative', 'function', 'z', 'continuous', 'student', 'triangular', 'continuous', 'range', 'function', 'triangular', 'wolfram', 'triangular', 'mode', 'triangular', 'continuous', 'triangle', 'uniform', 'difference', 'continuous', 'uniform', 'uniform', 'uniform', 'product', 'uniform', 'ratio', 'uniform', 'sum', 'rectangular', 'rectangular', 'constant', 'cumulative', 'function', 'uniform', 'interval', 'continuous', 'characteristic', 'uniform', 'continuous', 'continuous', 'continuous', 'discrete', 'uniform', 'equidistributed', 'triangular', 'uniform', 'difference', 'uniform', 'product', 'uniform', 'ratio', 'uniform', 'sum', 'product', 'plotted', 'product', 'continuous', 'uniform', 'difference', 'uniform', 'uniform', 'uniform', 'ratio', 'uniform', 'sum', 'function', 'ratio', 'continuous', 'ratio', 'ratio', 'uniform', 'difference', 'uniform', 'uniform', 'uniform', 'product', 'uniform', 'sum', 'sum', 'uniform', 'sum', 'sum', 'continuous', 'uniform', 'difference', 'uniform', 'uniform', 'uniform', 'product', 'uniform', 'ratio', 'range', 'order', 'function', 'mises', 'circular', 'mises', 'continuous', 'wald', 'continuous', 'inverse', 'gaussian', 'weibull', 'wolfram', 'moment', 'form', 'mendenhall', 'weibull', 'weibull', 'lifetimes', 'weibull', 'continuous', 'extreme', 'value', 'gumbel', 'gumbel', 'galton', 'bernoulli', 'discrete', 'two', 'written', 'bernoulli', 'wolfram', 'trial', 'bernoulli', 'bernoulli', 'bernoulli', 'simplest', 'building', 'number', 'number', 'number', 'number', 'bernoulli', 'discrete', 'bernoulli', 'binomial', 'coin', 'geometric', 'negative', 'binomial', 'run', 'binomial', 'distributed', 'parameter', 'parameter', 'beta', 'coefficient', 'binomial', 'discrete', 'beta', 'beta', 'binomial', 'binomial', 'binomial', 'discrete', 'successes', 'binomial', 'binomial', 'plot', 'successes', 'binomial', 'wolfram', 'binomial', 'beta', 'binomial', 'papoulis', 'function', 'random', 'binomial', 'large', 'treating', 'binomial', 'binomial', 'approximated', 'fixed', 'binomial', 'binomial', 'binomial', 'discrete', 'binomial', 'hypergeometric', 'negative', 'binomial', 'normal', 'normal', 'poisson', 'poisson', 'random', 'discrete', 'discrete', 'probability', 'over', 'discrete', 'discrete', 'bernoulli', 'bernoulli', 'binomial', 'binomial', 'continuous', 'continuous', 'geometric', 'geometric', 'hypergeometric', 'hypergeometric', 'negative', 'binomial', 'poisson', 'poisson', 'probability', 'statistical', 'uniform', 'uniform', 'likely', 'set', 'probability', 'function', 'function', 'uniform', 'discrete', 'uniform', 'wolfram', 'uniform', 'uniform', 'discrete', 'discrete', 'discrete', 'uniform', 'uniform', 'outcome', 'discrete', 'uniform', 'uniform', 'number', 'care', 'actual', 'binomial', 'binomial', 'normal', 'normal', 'random', 'geometric', 'discrete', 'probability', 'function', 'geometric', 'only', 'discrete', 'authors', 'prefer', 'form', 'form', 'above', 'case', 'number', 'geometric', 'subsequent', 'geometric', 'floor', 'geometric', 'discrete', 'geometric', 'hypergeometric', 'saint', 'probability', 'most', 'tail', 'discrete', 'bernoulli', 'bernoulli', 'coin', 'coin', 'hypergeometric', 'wolfram', 'hypergeometric', 'written', 'hypergeometric', 'discrete', 'multichoose', 'random', 'lattice', 'discrete', 'logarithmic', 'logarithmic', 'work', 'distinct', 'log-series', 'series', 'discrete', 'log', 'normal', 'logarithmic', 'logarithmic', 'quantities', 'mean', 'discrete', 'mean', 'variance', 'joint', 'multinomial', 'multinomial', 'coefficient', 'multinomial', 'discrete', 'binomial', 'binomial', 'multinomial', 'pascal', 'pascal', 'pelya', 'probability', 'coefficient', 'binomial', 'wolfram', 'binomial', 'discrete', 'binomial', 'binomial', 'viewing', 'viewing', 'function', 'large', 'poisson', 'poisson', 'papoulis', 'poisson', 'wolfram', 'poisson', 'normalized', 'poisson', 'reaches', 'poisson', 'papoulis', 'poisson', 'papoulis', 'poisson', 'poisson', 'poisson', 'expressed', 'poisson', 'two', 'poisson', 'parameter', 'poisson', 'been', 'form', 'number', 'poisson', 'poisson', 'discrete', 'binomial', 'binomial', 'erlang', 'erlang', 'poisson', 'large', 'poisson', 'poisson', 'point', 'poisson', 'zeta', 'discrete', 'zipf', 'zipf', 'zeta', 'discrete', 'discrete', 'function', 'zipf', 'wolfram', 'variance', 'mean', 'zipf', 'discrete', 'zipf', 'cumulative', 'function', 'general', 'function', 'function', 'cumulative', 'function', 'number', 'function', 'p', 'function', 'derivative', 'function', 'similarly', 'function', 'neither', 'joint', 'multivariate', 'function', 'evaluation', 'function', 'bivariate', 'function', 'normal', 'constant', 'method', 'value', 'maximum', 'maximum', 'method', 'function', 'cumulative', 'bivariate', 'function', 'marginal', 'joint', 'function', 'function', 'multiple', 'function', 'joint', 'function', 'general', 'function', 'satisfies', 'one', 'exponential', 'exponential', 'geometric', 'geometric', 'kurtosis', 'kurtosis', 'domain', 'joint', 'ratio', 'function', 'ratio', 'ratio', 'cauchy', 'uniform', 'ratio', 'ratio', 'general', 'cauchy', 'cauchy', 'difference', 'difference', 'product', 'product', 'sum', 'sum', 'uniform', 'ratio', 'two-dimensional', 'function', 'marginal', 'univariate', 'two-dimensional', 'function', 'copula', 'class', 'allowing', 'stable', 'general', 'variable', 'occur', 'cumulative', 'formally', 'normalized', 'measure', 'random', 'statistical', 'generalized', 'statistical', 'general', 'continuous', 'continuous', 'discrete', 'discrete', 'discrete', 'function', 'probability', 'real', 'power', 'function', 'general', 'function', 'normal', 'single', 'unimodal', 'general', 'bimodal', 'bimodal', 'unimodal', 'probability', 'cumulative', 'function', 'under', 'condition', 'normal', 'cramer', 'cramer', 'normal', 'squared', 'cochran', 'le', 'bernoulli', 'variance', 'consisting', 'equivalently', 'zero', 'normal', 'normal', 'function', 'independent')
based	('distribution', 'observed', 'distribution', 'set', 'statistical', 'outcome', 'estimate', 'estimate', 'estimation', 'linear', 'estimation', 'maximum', 'estimation', 'rank', 'r-estimates', 'statistical', 'mean', 'population', 'proximate', 'distance', 'algorithm', 'technique', 'linear', 'opposed', 'number', 'distribution', 'observed', 'occurring', 'information', 'down', 'previous', 'model', 'random', 'fit', 'perpendicular', 'fit', 'perpendicular', 'adjusted', 'value', 'inflation', 'price', 'particularly', 'selection', 'certain', 'fact', 'theory', 'type')
observed	('based', 'obtain', 'likelihood', 'distribution', 'table', 'frequency', 'variables', 'frequencies', 'comparing', 'frequency', 'sampling', 'compares', 'value', 'sample', 'equal', 'value', 'equal', 'based', 'likelihood', 'whereas', 'etc', 'first', 'wigner', 'coefficient', 'variance', 's', 'best-fitting', 'mean', 'mean', 'mean', 'distribution', 'frequencies', 'variable', 'independence', 'table', 'one', 'null', 'value', 'effect', 'discrepancy', 'expected', 'distribution', 'equal', 'value', 'affairs', 'test', 'great', 'unbiased', 'two', 'function', 'value', 'two', 'two', 'smaller', 'value', 'probability', 'successes', 'successes', 'binomial', 'model', 'clustering')
begin	('distribution', 'prior', 'database', 'cumulant', 'rewrite', 'follow', 'noting')
prior	('begin', 'values', 'distribution', 'function', 'valid', 'likelihood', 'distribution', 'language', 'language', 'language', 'occurring', 'time', 'time', 'time', 'strictly', 'time', 'liam', 'perspective', 'distribution')
anything	('including', 'subject')
including	('anything', 'assessment', 'quartile', 'top', 'even', 'properties', 'scaling', 'point', 'starting', 'point', 'starting', 'curve', 'cumulative', 'parameter', 'setup', 'elasticity')
assessment	('including', 'relative')
relative	('assessment', 'likelihoods', 'distribution', 'frequency', 'frequency', 'cumulative', 'frequency', 'frequency', 'cumulative', 'distribution', 'cumulative', 'frequency', 'frequency', 'frequency', 'frequency', 'cumulative', 'histogram', 'frequency', 'frequency', 'cumulative', 'point', 'cumulative', 'distribution', 'frequency', 'distribution', 'frequency', 'distribution', 'cumulative', 'error', 'error', 'accuracy', 'precision', 'error', 'error', 'error', 'error', 'precision', 'error', 'time', 'percent', 'error', 'precision', 'error', 'value', 'error', 'error', 'error', 'sum', 'time', 'error', 'error', 'error', 'deviation', 'deviation', 'deviation', 'deviation', 'quantities', 'deviation', 'deviation', 'deviation', 'measure', 'lebesgue', 'process', 'borel', "outcomes'", 'estimated', 'importance', 'ogive', 'cumulative', 'frequency', 'frequency', 'distribution', 'tries', 'description')
likelihoods	('relative', 'parameters')
results	('parameters', 'non-bayesian', 'header', 'random', 'meaningful', 'sampling', 'tossing', 'dimension', 'platonic', 'using', 'walk', 'randomly', 'acceptable', 'using', 'value', 'discontinuous', 'procedure', 'outlying', 'connection', 'two', 'distribution', 'variable', 'distribution', 'variable', 'analogous', 'hold', 'grains', 'summarized', 'actual')
non-bayesian	('results',)
practice	('common', 'positive', 'formula', 'due', 'common', 'playing', 'common', 'common', 'variate', 'common', 'transform', 'pearson', 'field', 'term', 'people')
common	('practice', 'uniform', 'most', 'objects', 'property', 'other', 'statistical', 'test', 'test', 'several', 'quantile', 'number', 'most', 'word', 'most', 'processor', 'distinction', 'source', 'number', 'most', 'underlying', 'distinction', 'source', 'most', 'use', 'quote', 'run', 'practice', 'distribution', 'law', 'practice', 'shooter', 'small', 'number', 'law', 'practice', 'most', 'example', 'constant', 'practice', 'most', 'form', 'most', 'type', 'plot', 'study', 'population', 'universes', 'variance', 'series', 'most', 'continuous', 'most', 'type', 'most', 'type', 'many', 'attributes', 'most', 'discrete')
uniform	('common', 'distribution', 'distribution', 'continuous', 'distribution', 'discrete', 'distribution', 'discrete', 't', 'assumed', 'throughout', 'statistic', 'distribution', 'continuous', 'set', 'discrepancy', 'distribution', 'girko', 'sequence', 'distribution', 'unfolding', 'distribution', 'ordinary', 'random', 'two', 'random', 'number', 'distribution', 'mean', 'pair', 'random', 'picking', 'distribution', 'distribution', 'distribution', 'distribution', 'stochastic', 'distribution', 'sequence', 'distribution', 'distribution', 'sequence', 'distribution', 'sequence', 'distribution', 'taken', 'distribution', 'variate', 'taken', 'variate', 'student', 'distribution', 'continuous', 'variate', 'logistic', 'linear', 'function', 'distribution', 'two', 'function', 'difference', 'distribution', 'distribution', 'distribution', 'product', 'distribution', 'ratio', 'distribution', 'sum', 'continuous', 'distribution', 'continuous', 'excess', 'distribution', 'discrete', 'distribution', 'distribution', 'difference', 'distribution', 'product', 'distribution', 'ratio', 'distribution', 'sum', 'product', 'yellow', 'product', 'distribution', 'difference', 'distribution', 'distribution', 'distribution', 'ratio', 'distribution', 'sum', 'ratio', 'diverge', 'ratio', 'distribution', 'difference', 'distribution', 'distribution', 'distribution', 'product', 'distribution', 'sum', 'sum', 'number', 'distribution', 'a090611', 'sum', 'distribution', 'difference', 'distribution', 'distribution', 'distribution', 'product', 'distribution', 'ratio', 'statistic', 'distribution', 'discrete', 'distribution', 'discrete', 'distribution', 'discrete', 'distribution', 'deviation', 'distribution', 'discrete', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'ratio', 'distribution', 'ratio')
over	('distribution', 'appropriate', 'probability', 'possible', 'distribution', 'nonnegative', 'interval', 'one', 'interval', 'advantages', 'fixed', 'matrices', 'matrices', 'matrices', 'matrices', 'small', 'matrices', 'stochastic', 'matrices', 'stochastic', 'taken', 'domain', 'periodic', 'interval', 'integral', 'sine', 'coin', 'record', 'history', 'one', 'probability', 'generated', 'occurrence', 'time', 'generated', 'run', 'integrating', 'upper', 'number', 'specified', 'space', 'hilbert', 'averaging', 'pass', 'number', 'displacement', 'self-avoiding', 'variable', 'normalized', 'distribution', 'interval', 'distribution', 'unit', 'distribution', 'probability', 'distribution', 'range', 'function', 'interval', 'function', 'function', 'distribution', 'ball', 'funnel', 'summation', 'total', 'argument', 'among', 'denoted', 'map', 'statistical')
appropriate	('over', 'range', 'case', 'use', 'statistic', 'seem', 'quantity', 'language', 'labeling', 'next', 'column', 'value', 'individual', 'value', 'individual', 'distributed', 'function', 'evaluation')
range	('appropriate', 'values', 'wolfram', 'interquartile', 'pearson', 'p', 'data', 'data', 'minimum', 'interquartile', 'step', 'interquartile', 'interquartile', 'interquartile', 'descriptive', 'above', 'sample', 'sample', 'divide', 'interquartile', 'percentile', 'quartile', 'interquartile', 'quartile', 'quartile', 'quartile', 'interquartile', 'quartile', 'quartile', 'statistic', 'random', 'sample', 'estimator', 'distribution', 'above', 'statistical', 'descriptive', 'midrange', 'statistical', 'fall', 'quantity', 'fall', 'concepts', 'momental', 'deviation', 'confidence', 'standard', 'probability', "wasn't", 'distribution', 'domain', 'reinhardt', 'statistical', 'surjection', 'denoted', 'element', 'distribution', 'probability', 'one', 'quantile', 'number', 'interpreting', 'specified', 'without', 'denoted', 'element', 'normal', 'normal', 'point', 'end', 'interquartile', 'quartile', 'variate', 'bin', 'variate', 'continuous', 'over', 'using', 'value', 'probability', 'value', 'neither', 'distribution', 'probability', 'distribution', 'probability', 'domain', 'image', 'image', 'form', 'statistical', 'statistical', 'general', 'segment', 'map', 'statistical', 'transformation')
values	('range', 'prior', 'multiply', 'posterior')
collect	('distribution', 'data')
data	('collect', 'obtain', 'number', 'points', 'applies', 'value', 'depend', 'digit', 'several', 'interval', 'point', 'bowley', 'value', 'binned', 'example', 'range', 'falling', 'range', 'frequency', 'benefit', 'presented', 'performed', 'contingency', 'tukey', 'raw', 'dividing', 'number', 'elements', 'distribution', 'set', 'size', 'mean', 'mean', 'alternatively', 'ordered', 'set', 'ordering', 'increasing', 'set', 'two', 'number', 'number', 'size', 'using', 'example', 'set', 'similarly', 'set', 'set', 'wolfram', 'empirical', 'outliers', 'best', 'proportion', 'set', 'denoted', 'number', 'number', 'statistical', 'list', 'function', 'structures', 'input', 'power', 'list', 'original', 'charlier', 'list', 'sample', 'set', 'set', 'mean', 'loading', 'loading', 'pearson', 'distributed', 'been', 'list', 'again', 'normally', 'list', 'estimated', 'set', 'variance', 'variance', 'linear', 'classification', 'classification', 'elements', 'collection', 'elements', 'season', 'small', 'fit', 'absence', 'distribution', 'make', 'because', 'interval', 'no', 'present', 'segmented', 'group', 'disappears', 'reverse', 'model', 'localized', 'model', 'localized', 'joke', 'statistic', 'rank', 'correlation', 'set', 'noisy', 'shown', 'coincide', 'deviation', 'uncertainties', 'noisy', 'transform', 'line', 'set', 'uncertainties', 'agreement', 'fitting', 'set', 'number', 'number', 'bar', 'plot', 'plotting', 'present', 'sample', 'coefficient', 'transforming', 'invented', 'number', 'extreme', 'small', 'number', 'number', 'grouping', 'histogram', 'categories', 'line', 'wolfram', 'pie', 'two', 'wolfram', 'summarizes', 'maintaining', 'individual', 'element', 'removing', 'wolfram', 'above', 'set', 'two', 'splitting', 'two', 'wolfram', 'exist', 'fisher', 'been', 'compare', 'except', 'parametric', 'type', 'conventional', 'set', 'moving', 'slutzky', 'set', 'make', 'analysis', 'ordered', 'time', 'collected', 'forecast', 'observation', 'once', 'longitudinal', 'longitudinal', 'astronomical', 'havil', 'analysis', 'surrogate', 'artificially', 'generated', 'mimic', 'isospectral', 'real', 'randomized', 'white', 'theorem', 'influenced')
obtain	('data', 'observed', 'normalize', 'unit', 'measurements', 'records', 'equation', 'inverse', 'variable', 'differentiate', 'straightforward', 'other', 'first', 'necessary', 'function', 'first', 'equation', 'working', 'order', 'correct', 'order', 'unbiased', 'integral', 'explicit', 'finally', 'size', 'statistically', 'first', 'people', 'oeis', 'grid', 'accurate', 'matrix', 'equation', 'guess', 'linearized', 'append', 'sequence', 'adding', 'adding', 'adding', 'sequence', 'term', 'asymptotic', 'product', 'row', 'simpler', 'function', 'fourier', 'care', 'idealized')
calculate	('distribution', 'tells', 'estimate', 'tells', 'possible', 'using', 'observation', 'size', 'binomial', 'observation', 'formula', 'probability', 'observation', 'row', 'matrix', 'conditional', 'one', 'conditional', 'test', 'cumulative', 'class', 'cumulative', 'freedom', 'maximum', 'model')
likelihood	('observed', 'multiply', 'function', 'maximum', 'prior', 'standard', 'defining', 'field', 'matrix', 'matrix', 'function', 'log', 'function', 'maximum', 'mean', 'maximum', 'maximum', 'distribution', 'maximum', 'estimate', 'maximum', 'ahead', 'time', 'maximum', 'standard', 'maximum', 'analysis', 'analysis', 'function', 'maximum', 'estimator', 'maximum', 'estimator', 'parameter', 'maximum', 'estimator', 'estimator', 'function', 'maximum', 'method', 'maximum', 'maximum', 'maximum', 'estimator', 'hypothetical', 'event', 'refers', 'outcome', 'probability', 'graph', 'graph', 'function', 'function', 'ratio', 'maximum', 'maximum', 'maximum', 'estimator', 'negative', 'ratio', 'function', 'p', 'function', 'probability', 'probability', 'ratio', 'maximum', 'logarithm', 'defining', 'log', 'function', 'probability', 'probability', 'function', 'statistic', 'probability', 'index', 'moving', 'probability', 'observed', 'term', 'term', 'ratio', 'follow', 'ratio', 'negative', 'ratio', 'observing', 'compare', 'nested', 'log', 'procedure', 'negative', 'ratio', 'negative', 'ratio', 'test', 'ratio', 'log', 'procedure', 'test', 'ratio', 'log', 'procedure', 'negative', 'ratio', 'maximum', 'moving', 'equal')
function	('distribution', 'parameter', 'likelihood', 'prior', 'density', 'above', 'distance', 'curve', 'reaches', 'apodization', 'maximum', 'lorenz', 'curve', 'cumulative', 'distribution', 'ordered', 'quantile', 'similar', 'quantile', 'assigns', 'value', 'ceiling', 'fractional', 'estimated', 'quantile', 'quantile', 'quantile', 'random', 'score', 'partial', 'standard', 'defining', 'using', 'score', 'extensive', 'score', 'probability', 'likelihood', 'logarithm', 'likelihood', 'partial', 'value', 'extreme', 'language', 'slower', 'slower', 'c', 'data', 'modify', 'interval', 'following', 'following', 'rational', 'margin', 'integer', 'precision', 'value', 'variable', 'single', 'rearranging', 'likelihood', 'maximum', 'maximum', 'likelihood', 'probability', 'taken', 'feller', 'taken', 'density', 'similarly', 'characteristic', 'indicator', 'indicator', 'identically', 'denoted', 'characteristic', 'repeating', 'characteristic', 'special', 'term', 'characteristic', 'different', 'using', 'characteristic', 'characteristic', 'converges', 'papoulis', 'characteristic', 'generate', 'characteristic', 'generating', 'probability', 'density', 'set', 'simple', 'fourier', 'using', 'characteristic', 'cumulant', 'generating', 'fourier', 'cumulant', 'generating', 'cumulant', 'independent', 'cumulant-generating', 'cumulant', 'generating', 'generating', 'property', 'term', 'quantity', 'necessarily', 'central', 'moment', 'centroid', 'beta', 'gamma', 'euler-mascheroni', 'moment', 'characteristic', 'charlier', 'generating', 'factorial', 'generating', 'moment', 'denotes', 'continuous', 'moment-generating', 'satisfies', 'cumulant-generating', 'moment', 'generating', 'characteristic', 'cumulant', 'cumulant', 'generating', 'moment', 'possible', 'bounded', 'sequence', 'bounded', 'skewness', 'incorrectly', 'first', 'population', 'probability', 'taken', 'obtain', 'probability', 'similarly', 'similarly', 'periodic', 'conjecture', 'distribution', 'consistent', 'kenney', 'pp', 'plotted', 'p', 'statistical', 'bivariate', 'normally', 'density', 'bivariate', 'singular', 'cluster', 'background', 'time', 'governs', 'density', 'exciting', 'exciting', 'excitation', 'excitation', 'intensity', 'rewrite', 'intensity', 'non-linear', 'assumed', 'collection', 'context', 'univariate', 'immigrant', 'intensity', 'form', 'multivariate', 'intensity', 'multivariate', 'multivariate', 'point', 'univariate', 'multivariate', 'multivariate', 'multivariate', 'standardized', 'univariate', 'univariate', 'unknown', 'expressing', 'curve', 'relevant', 'density', 'density', 'use', 'kernel', 'order', 'distribution', 'probability', 'probability', 'rose', 'recursive', 'grows', 'explicit', 'approximation', 'diaconis', 'distance', 'intensity', 'time', 'example', 'real', 'domain', 'sent', 'probability', 'domain', 'distribution', 'available', 'excitation', 'time', 'exciting', 'time', 'hazard', 'hazard', 'hazard', 'failure', 'survival', 'distribution', 'evans', 'hazard', 'probability', 'density', 'survival', 'survival', 'hazard', 'intensity', 'theory', 'authors', 'intensity', 'intensity', 'point', 'intensity', 'time', 'intensity', 'intensity', 'pawlas', 'intensity', 'intensity', 'intensity', 'point', 'likelihood', 'likelihood', 'likelihood', 'probability', 'probability', 'likelihood', 'probability', 'log-likelihood', 'natural', 'expanded', 'log-likelihood', 'throughout', 'likelihood', 'probability', 'likelihood', 'logarithm', 'distribution', 'joint', 'distribution', 'probability', 'density', 'survival', 'probability', 'distribution', 'latter', 'particularly', 'distribution', 'hazard', 'hazard', 'probability', 'density', 'survival', 'survival', 'probability', 'normalized', 'probability', 'cumulative', 'cumulative', 'distribution', 'independent', 'density', 'probability', 'density', 'probability', 'probability', 'satisfies', 'probability', 'set', 'sum', 'probability', 'delta', 'probability', 'distribution', 'probability', 'ratio', 'probability', 'probability', 'normal', 'density', 'probability', 'distribution', 'joint', 'distribution', 'product', 'probability', 'continuous', 'quantile', 'quantile', 'quantile', 'denotes', 'quantile', 'probability', 'distribution', 'monotone', 'monotonic', 'probability', 'probability', 'density', 'quantile', 'probability', 'conclude', 'inflection', 'beta', 'edelman', 'probability', 'number', 'generalized', 'erf', 'exponential', 'upper', 'integrating', 'matrices', 'measurable', 'probability', 'domain', 'stochastic', 'interestingly', 'value', 'variance', 'gamma', 'closed', 'bessel', 'first', 'ratio', 'abbott', 'induced', 'language', 'inversion', 'gamma', 'kenney', 'kenney', 'merit', 'regression', 'merit', 'fitting', 'independent', 'pendulum', 'length', 'form', 'convergence', 'nonlinear', 'outset', 'point', 'procedure', 'minimize', 'applying', 'fitting', 'independent', 'point', 'minimized', 'value', 'continuous', 'figure-of-merit', 'figure-of-merit', 'merit', 'small', 'merit', 'smallest', 'merit', 'best-fit', 'merit', 'regression', 'closely', 'rational', 'minimax', 'variable', 'value', 'analytic', 'convergence', 'shown', 'actual', 'merit', 'multiple', 'fraction', 'number', 'feller', 'characteristic', 'formal', 'developing', 'standard', 'edgeworth', 'distribution', 'expansion', 'width', 'number', 'gaussian', 'histogram', 'find', 'density', 'asymptotically', 'observation', 'number', 'shah', 'sinc', 'sinc', 'probability', 'distribution', 'beta', 'regularized', 'beta', 'confluent', 'hypergeometric', 'first', 'probability', 'beta', 'fermi', 'sigmoid', 'inverse', 'distribution', 'distribution', 'th', 'density', 'distribution', 'cumulative', 'distribution', 'incomplete', 'regularized', 'chi-squared', 'hypergeometric', 'second', 'natural', 'distribution', 'joins', 'form', 'two-dimensional', 'copula', 'copula', 'correlation', 'spectral', 'waiting', 'incomplete', 'explicitly', 'probability', 'closely', 'error', 'distribution', 'distribution', 'wolfram', 'heaviside', 'fourier', 'probability', 'characteristic', 'central', 'distribution', 'gamma', 'abramowitz', 'probability', 'cumulative', 'distribution', 'gamma', 'beta', 'regularized', 'hypergeometric', 'wolfram', 'beta', 'gamma', 'gamma', 'hotelling', 'beta', 'snedecor', 'sigmoid', 'sigmoid', 'waiting', 'incomplete', 'probability', 'waiting', 'probability', 'gamma', 'distribution', 'regularized', 'wolfram', 'language', 'describing', 'logarithmic', 'beta', 'cumulant-generating', 'distribution', 'distribution', 'probability', 'distribution', 'distribution', 'th', 'probability', 'wolfram', 'first', 'distribution', 'mean', 'bessel', 'second', 'density', 'cumulative', 'wolfram', 'gamma', 'using', 'abramowitz', 'log', 'wolfram', 'probability', 'distribution', 'distribution', 'applies', 'correcting', 'similar', 'lorentzian', 'sigmoid', 'sigmoid', 'distribution', 'airy', 'maxwell', 'bessel', 'first', 'wolfram', 'doubly', 'beta', 'hypergeometric', 'th', 'beta', 'generalized', 'confluent', 'hypergeometric', 'first', 'normal', 'domain', 'probability', 'erf', 'error', 'neither', 'probability', 'normal', 'normal', 'computed', 'normal', 'error', 'distribution', 'gaussian', 'half', 'distribution', 'normal', 'owen', 'pearson', 'tetrachoric', 'distribution', 'probability', 'erf', 'error', 'probability', 'approximated', 'different', 'distribution', 'feller', 'p', 'less', 'distribution', 'continuous', 'hh', 'normal', 'owen', 'probability', 'tetrachoric', 'modified', 'bessel', 'second', 'density', 'bivariate', 'normal', 'inverse', 'linear', 'normally', 'standard', 'density', 'distribution', 'distribution', 'over', 'regularized', 'beta', 'first', 'standardized', 'radiation', 'radiation', 'normalized', 'normalized', 'without', 'radiation', 'continuous', 'arbitrary', 'expected', 'observed', 'probability', 'distribution', 'parameter', 'first', 'rayleigh', 'bessel', 'first', 'solution', 'beta', 'distribution', 'over', 'absolute', 'distribution', 'probable', 'tetrachoric', 'number', 'beta', 'hypergeometric', 'regularized', 'first', 'bessel', 'second', 'density', 'student', 'distribution', 'modified', 'bessel', 'second', 'distribution', 'triangle', 'uniform', 'heaviside', 'uniform', 'density', 'cumulative', 'distribution', 'latter', 'characteristic', 'simplifies', 'moment-generating', 'differentiable', 'rectangle', 'triangular', 'heaviside', 'distribution', 'elegant', 'obtain', 'density', 'modified', 'bessel', 'first', 'distribution', 'cannot', 'slightly', 'written', 'bernoulli', 'moment-generating', 'raw', 'beta', 'binomial', 'gamma', 'generalized', 'incomplete', 'characteristic', 'binomial', 'distribution', 'logarithm', 'probability', 'over', 'population', 'distribution', 'cumulative', 'distribution', 'discrete', 'distribution', 'geometric', 'first', 'first', 'geometric', 'generating', 'oeis', 'hypergeometric', 'hypergeometric', 'incomplete', 'log-series', 'probability', 'nonnegative', 'binomial', 'gamma', 'regularized', 'regularized', 'negative', 'moment-generating', 'raw', 'distribution', 'expected', 'same', 'poisson', 'poisson', 'mean', 'poisson', 'generalization', 'positive', 'distribution', 'generalized', 'mean', 'distribution', 'general', 'distribution', 'distribution', 'cumulative', 'distribution', 'probability', 'distribution', 'denoted', 'distribution', 'continuous', 'distribution', 'distribution', 'discrete', 'distribution', 'appropriate', 'distribution', 'possible', 'distribution', 'probability', 'inverse', 'distribution', 'general', 'density', 'survival', 'survival', 'variate', 'distribution', 'marginal', 'satisfies', 'distribution', 'distribution', 'two', 'probability', 'satisfies', 'distribution', 'distribution', 'general', 'distribution', 'density', 'ratio', 'distribution', 'probability', 'probability', 'outer', 'distribution', 'marginal', 'copula', 'two-dimensional', 'distribution', 'trial', 'describing', 'abbreviated', 'pdf', 'describing', 'cumulative', 'abbreviated', 'sense', 'statistical', 'distribution', 'generalized', 'generalized', 'measurable', 'density', 'random', 'survival', 'probability', 'survival', 'continuous', 'survival', 'discrete', 'survival', 'distribution', 'probability', 'survival', 'general', 'distribution', 'distribution', 'normal', 'abramowitz', 'lindeberg', 'distribution')
parameter	('function', 'distribution', 'fwhm', 'width', 'statistic', 'estimate', 'denoted', 'value', 'likelihood', 'denoted', 'symbol', 'equivalent', 'actually', 'freedom', 'wishart', 'two', 'lacks', 'representing', 'perlman', 'size', 'short', 'size', 'binomial', 'point', 'length', 'density', 'harris', 'underlying', 'using', 'linear', 'without', 'nonlinear', 'using', 'adjusted', 'smallest', 'press', 'overdetermined', 'initial', 'edgeworth', 'papoulis', 'including', 'best-fit', 'value', 'against', 'allowed', 'labeled', 'cauchy', 'most', 'generalized', 'location', 'scale', 'scale', 'wolfram', 'labeled', 'moment-generating', 'distributed', 'independent', 'beta', 'derived', 'variate', 'gamma', 'variate', 'gamma', 'location', 'scale', 'scale', 'wolfram', 'mean', 'limited', 'denoted', 'dimensionality', 'number', 'inverse', 'noncentrality', 'modified', 'written', 'function', 'wolfram', 'taken', 'von', 'distribution', 'distribution', 'conditional', 'most', 'poisson', 'distribution', 'seen', 'positive', 'riemann', 'skewness', 'scale', 'scale', 'location', 'location', 'two')
multiply	('values', 'likelihood')
normalize	('distribution', 'obtain', 'necessary')
unit	('obtain', 'probability', 'universal', 'solve', 'walk', 'bivariate', 'distribution', 'set', 'distributed', 'set', 'distributed', 'set', 'dimension', 'random', 'square', 'step', 'distance', 'step', 'per', 'period', 'geometric', 'per', 'period', 'per', 'period', 'estimated', 'per', 'period', 'per', 'period', 'marshall', 'per', 'period', 'per', 'period', 'per', 'period', 'over', 'interval', 'mean', 'covariance', 'distribution', 'scale', 'mean', 'one-dimensional', 'length', 'expectation', 'variance')
probability	('unit', 'over', 'event', 'greater', 'universal', 'distribution', 'proper', 'distribution', 'cutoffs', 'first', 'basic', 'example', 'person', 'cup', 'random', 'table', 'person', 'conditional', 'person', 'conditional', 'frequency', 'event', 'sample', 'vector', 'distribution', 'specific', 'assigns', 'attained', 'certain', 'density', 'regions', 'position', 'paper', 'greater', 'next', 'fact', 'density', 'function', 'derivative', 'derivative', 'variance', 'distribution', 'density', 'language', 'encountering', 'confidence', 'symmetric', 'density', 'distribution', 'measurement', 'variable', 'density', 'conditional', 'independent', 'distribution', 'matrix', 'matrix', 'transition', 'moment', 'function', 'distribution', 'univariate', 'density', 'multivariate', 'density', 'denoted', 'transform', 'density', 'case', 'density', 'function', 'density', 'transform', 'density', 'necessarily', 'density', 'variable', 'density', 'distribution', 'density', 'moment', 'function', 'multivariate', 'function', 'deviation', 'distribution', 'distribution', 'density', 'covariance', 'density', 'normal', 'joint', 'density', 'quadrant', 'special', 'process', 'self', 'variable', 'density', 'quadrant', 'special', 'coefficient', 'getting', 'craig', 'density', 'function', 'function', 'allowed', 'error', 'variable', 'variable', 'axioms', 'denotes', 'theorem', 'conditional', 'conditional', 'inclusion', 'total', 'theorem', 'no', 'birthday', 'second', 'factorial', 'two', 'general', 'birthday', 'people', 'birthday', 'people', 'least', 'mosteller', 'estimated', 'problem', 'birthday', 'true', 'least', 'relationship', 'unions', 'inequalities', 'disjoint', 'inequality', 'bonferroni', 'certain', 'event', 'infinite', 'case', 'none', 'particular', 'finite', 'lemma', 'find', 'needle', 'take', 'uspensky', 'thrown', 'needle', 'problem', 'buffon', 'find', 'needle', 'line', 'needle', 'line', 'noting', 'less', 'boundary', 'problem', 'buffon', 'luck', 'length', 'coin', 'coin', 'lie', 'equal', 'landing', 'grid', 'coin', 'similarly', 'coin', 'length', 'coin', 'coin', 'lie', 'length', 'coin', 'coin', 'lie', 'length', 'coin', 'tile', 'lie', 'problem', 'buffon', 'flipping', 'coin', 'coin', 'estimated', 'fair', 'flips', 'initial', 'head', 'confidence', 'see', 'seeing', 'hthh', 'gardner', 'hhh', 'gardner', 'coin', 'example', 'no', 'similarly', 'no', 'tossing', 'bernoulli', 'coincidence', 'birthday', 'reason', 'random', 'conditional', 'conditional', 'conditional', 'bayes', 'conjunctive', 'total', 'total', 'theorem', 'repeatedly', 'object', 'problem', 'birthday', 'getting', 'higher', 'least', 'time', 'throwing', 'problem', 'boxcars', 'range', 'theory', 'et', 'function', 'density', 'sense', 'density', 'domain', 'codomain', 'over', 'domain', 'space', 'sample', 'rate', 'hazard', 'two', 'happen', 'first', 'happen', 'second', 'conjunctive', 'conjunctive', 'conditional', 'conditional', 'mortality', 'hazard', 'player', 'indefinitely', 'ruin', 'coin', 'ratio', 'density', 'function', 'mills', 'ratio', 'density', 'rate', 'hazard', 'satisfies', 'case', 'statistic', 'bayes', 'conditional', 'independent', 'process', 'axioms', 'axioms', 'axioms', 'event', 'differ', 'differ', 'refers', 'likelihood', 'graph', 'ratio', 'function', 'function', 'density', 'configuration', 'density', 'function', 'likelihood', 'likelihood', 'function', 'likelihood', 'likelihood', 'logarithm', 'marginal', 'marginal', 'marginal', 'marginal', 'conditional', 'conditional', 'distribution', 'function', 'density', 'variable', 'denotes', 'theorem', 'inequality', 'function', 'density', 'ratio', 'distribution', 'function', 'density', 'function', 'principle', 'mutually', 'event', 'newton', 'stigler', 'sixes', 'problem', 'de', 'correspond', 'winning', 'winning', 'odd', 'colon', 'variate', 'value', 'alpha', 'portion', 'distribution', 'point', 'point', 'tail', 'tail', 'space', 'sample', 'branch', 'governed', 'view', 'measure', 'treat', 'subjectively', 'assign', 'possible', 'interval', 'density', 'function', 'distribution', 'denoted', 'variate', 'assumption', 'already', 'generalized', 'generalized', 'bayes', 'conditional', 'countable', 'additivity', 'axiom', 'likelihood', 'axioms', 'axioms', 'density', 'function', 'inequality', 'event', 'exclusive', 'axiom', 'experiment', 'outcome', 'sample', 'density', 'function', 'function', 'find', 'function', 'similarly', 'distribution', 'function', 'similarly', 'function', 'distribution', 'function', 'distribution', 'function', 'asymptotic', 'function', 'stegun', 'density', 'function', 'continuous', 'function', 'density', 'distribution', 'domain', 'interval', 'domain', 'domain', 'range', 'superset', 'inequality', 'inequality', 'measure', 'normalized', 'measure', 'measure', 'measurable', 'measure', 'measure', 'space', 'measure', 'space', 'space', 'measurable', 'measure', 'measure', 'measure', 'mistakes', 'printer', 'monotonic', 'density', 'assign', 'attained', 'function', 'continuous', 'function', 'function', 'density', 'function', 'fact', 'firing', 'revolver', 'first', 'roulette', 'noting', 'winning', 'seen', 'distribution', 'paradox', 'coin', 'space', 'outcome', 'outcome', 'space', 'variable', 'paradox', 'asks', 'two', 'problem', 'birthday', 'process', 'marked', 'statistic', 'box', 'comparison', 'residual', 'tail', 'likelihood', 'tail', 'tail', 'tail', 'tail', 'p', 'point', 'total', 'total', 'theorem', 'theorem', 'bayes', 'conditional', 'inclusion', 'lottery', 'fano', 'same', 'generating', 'halves', 'case', 'behavior', 'real', 'smallest', 'entire', 'function', 'matrices', 'one', 'function', 'domain', 'number', 'reason', 'space', 'variable', 'set', 'space', 'denoted', 'variate', 'random', 'line', 'step', 'right', 'step', 'examine', 'coefficient', 'particular', 'walk', 'traveling', 'unity', 'reaching', 'unity', 'reaching', 'infinity', 'reaching', 'law', 'interested', 'correlation', 'clump', 'run', 'pick', 'head', 'similarly', 'no', 'trial', 'success', 'general', 'occur', 'calculate', 'run', 'entries', 'entries', 'isolated', 'entries', 'entries', 'isolated', 'corollary', 'successes', 'estimate', 'event', 'pp', 'distribution', 'getting', 'hypergeometric', 'using', 'statistic', 'hypothesis', 'p-value', 'test', 'value', 'test', 'value', 'test', 'statistical', 'variate', 'determining', 'could', 'statistical', 'getting', 'measurement', 'statistical', 'sensitivity', 'test', 'joint', 'distribution', 'event', 'success', 'subset', 'set', 'satisfying', 'assigned', 'outcome', 'experiment', 'space', 'trial', 'success', 'subset', 'trial', 'success', 'shown', 'number', 'true', 'least', 'domain', 'function', 'distribution', 'function', 'n', 'density', 'freedom', 'density', 'success', 'great', 'density', 'densities', 'distribution', 'function', 'change', 'distribution', 'exponential', 'function', 'beta', 'density', 'domain', 'function', 'excess', 'large', 'distribution', 'function', 'written', 'function', 'beta', 'density', 'interval', 'function', 'function', 'distribution', 'domain', 'distribution', 'over', 'density', 'had', 'density', 'transform', 'addition', 'variable', 'density', 'variate', 'function', 'distribution', 'distribution', 'density', 'molecule', 'cumulative', 'distribution', 'density', 'distribution', 'density', 'function', 'standard', 'function', 'variate', 'function', 'variate', 'range', 'function', 'normal', 'interval', 'quantity', 'function', 'integral', 'joint', 'density', 'distribution', 'density', 'random', 'function', 'deviation', 'distribution', 'density', 'variance', 'density', 'error', 'integral', 'defining', 'cumulative', 'mean', 'difference', 'density', 'range', 'density', 'constant', 'density', 'noting', 'sum', 'range', 'density', 'labelled', 'labelled', 'labelled', 'density', 'fixed', 'success', 'estimator', 'observed', 'trial', 'density', 'discrete', 'true', 'false', 'false', 'binomial', 'n', 'successes', 'higher', 'hypergeometric', 'distribution', 'function', 'distribution', 'statistical', 'using', 'integer', 'distribution', 'left', 'symmetrically', 'turn', 'process', 'distribution', 'density', 'tail', 'distribution', 'selection', 'successful', 'finding', 'picking', 'asks', 'out', 'ball', 'correct', 'covariance', 'successful', 'expansion', 'density', 'variate', 'function', 'event', 'distribution', 'successes', 'trial', 'density', 'process', 'successes', 'out', 'interval', 'interval', 'one', 'trial', 'two', 'event', 'density', 'function', 'continuous', 'density', 'discrete', 'exist', 'depend', 'closed', 'integration', 'density', 'function', 'region', 'frequency', 'density', 'joint', 'function', 'opposite', 'value', 'density', 'joint', 'density', 'function', 'function', 'class', 'describing', 'value', 'occur', 'density', 'cumulative', 'value', 'value', 'setting', 'measure', 'measure', 'density', 'same', 'distribution', 'function', 'continuous', 'density', 'discrete', 'survival', 'function', 'arbitrary', 'distribution', 'addend', 'density', 'pair', 'better', 'number', 'theory', 'khinchin', 'average')
possible	('over', 'difference', 'pair', 'two', 'orderings', 'estimate', 'using', 'estimate', 'consisting', 'conditions', 'function', 'value', 'calculate', 'distribution', 'equally', 'out', "sevast'yanov", 'grid', 'coin', 'tosses', 'humanity', 'combination', 'studies', 'probability', 'outcome', 'contain', 'set', 'set', 'set', 'several', 'polyhedra', 'example', 'achieved', 'linearize', 'matrix', 'many', 'many', 'number', 'arrangements', 'one', 'find', 'other', 'matrices', 'tested', 'rejection', 'even', 'root', 'two', 'variable', 'value', 'function', 'extrema', 'two', 'time', 'outcome')
posterior	('values',)
mode	('distribution', 'term', 'distribution', 'multimodal', 'pearson', 'skewness', 'gauss', 'set', 'unique', 'single', 'one', 'multimodal', 'set', 'median', 'appears', 'pearson', 'skewness', 'rank', 'pearson', 'skewness', 'set', 'bimodal', 'trimodal', 'median', 'appears', 'pearson', 'midrange', 'order', 'pearson', 'skewness', 'kenney', 'trimodal', 'bimodal', 'multimodal', 'term', 'bimodal', 'multimodal', 'appears', 'pearson', 'pearson', 'skewness', 'standard', 'pearson', 'skewness', 'pearson', 'skewness', 'mean', 'pearson', 'standard', 'pearson', 'pearson', 'skewness', 'skewness', 'pearson', 'fisher', 'vanishes', 'symmetric', 'distribution')
analog	('bayesian', 'confidence', 'continuous', 'geometric', 'p', 'central', 'circular', 'normal', 'discrete', 'exponential')
confidence	('analog', 'interval', 'interval', 'probability', 'interval', 'mean', 'interval', 'probability-', 'interval', 'probability-', 'interval', 'hypothesistesting`', 'interval', 'analysis', 'endpoints', 'interval', 'limit', 'analysis', 'interval', 'estimate', 'percent', 'order', 'refers', 'analysis', 'interval', 'producing', 'list', 'range', 'moment', 'interval', 'landing', 'probability', 'harmonic', 'test', 'interval', 't', 'coincidence', 'interval', 'ci', 're', 'quantity', 'theorem', 'interval', 'table', 'p', 'goulden')
intervals	('using',)
using	('intervals', 'standard', 'law', 'number', 'easier', 'contingency', 'data', 'following', 'function', 'above', 'possible', 'little', 'computed', 'computed', 'zero', 'binomial', 'transformations', 'transformations', 'transformations', 'denoted', 'iverson', 'function', 'fourier', 'function', 'fourier', 'moment', 'calculation', 'statistic', 'computed', 'moment-generating', 'mean', 'inverse', 'transformations', 'transformations', 'calculate', 'recursion', 'computed', 'recurrence', 'distribution', 'transformed', 'variance', 'definition', 'expressed', 'covariance', 'statistic', 'only', 'computed', 'recurrence', 'computed', 'formula', 'proven', 'venn', 'number', 'linear', 'results', 'quasirandom', 'plugging', 'parameter', 'fit', 'results', 'normal', 'term', 'parameter', 'fit', 'point', 'unsquared', 'formula', 'solved', 'standard', 'point', 'goodness-of-fit', 'line', 'linear', 'indicated', 'rectangle', 'face', 'characteristics--head', 'generated', 'wolfram', 'involved', 'test', 'solution', 'best-fit', 'probability', 'sum', 'average', 'distribution', 'distribution', 'moment-generating', 'first', 'recursion', 'computed', 'characteristic', 'function', 'fourier', 'range', 'form', 'distribution', 'computed', 'named', 'pearson', 'computed', 'continued', 'derived', 'moment-generating', 'z', 'defining', 'probability', 'restricting', 'efficiently', 'continuous', 'distributed', 'random')
standard	('using', 'function', 'likelihood', 'deviation', 'deviation', 'population', 'modify', 'paper-and-pencil', 'within', 'significance', 'deviation', 'deviation', 'deviation', 'interval', 'erf', 'deviation', 'likelihood', 'sample', 'population', 'estimator', 'distribution', 'deviation', 'deviation', 'deviation', 'deviation', 'deviation', 'variance', 'cumulant', 'skewness', 'deviation', 'mean', 'deviation', 'statistic', 'other', 'statistical', 'namely', 'deviation', 'deviation', 'variance', 'skewness', 'deviation', 'mode', 'mode', 'deviation', 'deviation', 'synonym', 'mean', 'deviation', 'computation', 'deviation', 'skewness', 'deviation', 'deviation', 'sample', 'deviation', 'sample', 'deviation', 'variance', 'deviation', 'deviation', 'synonym', 'deviation', 'baseline', 'deviation', 'deviation', 'deviation', 'multiple', 'deviation', 'find', 'deviation', 'range', 'deviation', 'square', 'deviation', 'distribution', 'error', 'sample', 'p', 'deviation', 'distribution', 'deviation', 'definition', 'error', 'error', 'sample', 'estimate', 'distribution', 'error', 'p', 'error', 'mean', 'deviation', 'variance', 'sigma', 'error', 'mean', 'deviation', 'simplifies', 'normal', 'cumulant', 'taken', 'normal', 'element', 'normal', 'taken', 'normal', 'taken', 'normal', 'entries', 'normal', 'motion', 'easily', 'process', 'brownian', 'index', 'reason', 'pp', 'using', 'matrix', 'denotes', 'function', 'normal', 'doing', 'mean', 'se', 'proportion', 'normally', 'mean', 'mean', 'deviation', 'gamma', 'taken', 'normal', 'sigma', 'normal', 'converted', 'normal', 'probability', 'normal', 'distribution', 'normal', 'mean', 'function', 'form', 'significance', 'error', 'error', 'normal', 'normal', 'quartile', 'normal', 'error', 'normal', 'population', 'variate', 'normal', 'mean')
somewhat	('analysis', 'controversial', 'use', 'less', 'always', 'less')
controversial	('somewhat', 'because')
because	('controversial', 'validity', 'excess', 'normal', 'essentially', 'mean', 'definition', 'size', 'data', 'denoted', 'inclusion', 'revolver', 'mass', 'value', 'quantity', 'unfortunately', 'absolute', 'equation', 'normal', 'altman', 'answer', 'use', 'equal', 'less', 'distribution', 'curved', 'middle', 'occur', 'experimenter', 'think', 'mathematicians', 'believe')
validity	('because', 'depends')
depends	('validity', 'valid')
valid	('depends', 'prior', 'uniformly', 'edgeworth', 'hypothesis')
cannot	('distribution', 'assessed', 'language', 'access', 'derivative', 'treated', 'formulation', 'outcome', 'ahead', 'function', 'done', 'equation', 'solved')
assessed	('cannot',)
statistically	('season', 'top', 'rule', 'increases', 'independent', 'obtain', 'meaningful', 'variate', 'independent', 'independent', 'independent', 'case', 'significant', 'effect')
season	('statistically', 'episode', 'inference', 'episode', 'burglaries', 'running', 'formally', 'episode', 'chain', 'episode', 'data', 'pilot', 'episode', 'shooter', 'black')
episode	('season', 'man', 'season', 'judgment', 'man', 'television', 'season', 'sniper', 'season', 'man', 'season', 'dark')
man	('episode', 'episode', 'episode')
hunt	('television', 'television')
television	('hunt', 'crime', 'episode', 'crime', 'zero', 'crime', 'hunt', 'crime', 'matter', 'crime')
crime	('television', 'drama', 'television', 'drama', 'television', 'drama', 'television', 'drama', 'television', 'drama')
drama	('crime', 'crime', 'crime', 'crime', 'crime')
numb3rs	('featured', 'benford', 'mentions', 'features', 'feature')
featured	('numb3rs', 'bayesian', 'judgment', 'bayesian')
inference	('bayesian', 'season')
judgment	('episode', 'featured')
filtering	('bayesian',)
maximum	('analysis', 'likelihood', 'half', 'half', 'half', 'descriptive', 'function', 'theoretical', 'one', 'local', 'local', 'running', 'running', 'statistic', 'mean', 'running', 'high-water', 'running', 'descriptive', 'local', 'local', 'local', 'slight', 'error', 'estimator', 'likelihood', 'based', 'likelihood', 'likelihood', 'distribution', 'likelihood', 'distribution', 'likelihood', 'case', 'likelihood', 'distribution', 'likelihood', 'function', 'likelihood', 'likelihood', 'function', 'harris', 'p', 'likelihood', 'likelihood', 'estimator', 'likelihood', 'follow', 'likelihood', 'important', 'hinge', 'midrange', 'estimator', 'likelihood', 'ratio', 'likelihood', 'likelihood', 'likelihood', 'ratio', 'likelihood', 'point', 'smallest', 'deviation', 'dot', 'hatched', 'minimum', 'calculate', 'fitting', 'likelihood', 'half', 'statistical', 'decreasing', 'th', 'distribution', 'extreme', 'distribution', 'log-weibull', 'oeis', 'reaches', 'euler-mascheroni', 'distribution', 'distribution')
number	('data', 'anomalous', 'descriptive', 'invariant', 'variety', 'multiplication', 'variables', 'using', 'different', 'class', 'conjugacy', 'multiperfect', 'class', 'expected', 'men', 'event', 'class', 'computing', 'data', 'expected', 'high-water', 'comparison', 'records', 'above', 'records', 'a055980', 'measurements', 'even', 'data', 'odd', 'data', 'equations', 'population', 'distinct', 'total', 'throws', 'part', 'slightly', 'summarizes', 'common', 'total', 'data', 'total', 'data', 'rank', 'different', 'difference', 'quantities', 'accuracy', 'accuracy', 'significant', 'total', 'significant', 'largest', 'stored', 'get', 'get', 'division', 'division', 'creating', 'arbitrary', 'broken', 'terminating', 'arbitrary', 'fixed', 'accuracy', 'accuracy', 'significant', 'total', 'significant', 'product', 'quantities', 'expressed', 'notation', 'significant', 'figure', 'express', 'within', 'significant', 'significant', 'smallest', 'significant', 'subtraction', 'significant', 'variable', 'closed', 'table', 'distinct', 'excess', 'satisfies', 'wolfram', 'under', 'skewness', 'common', 'point', 'large', 'count', 's', 's', 'sample', 'sample', 'peterson', 'people', 'smallest', 'people', 'minimal', 'people', 'approximation', 'people', 'asks', 'people', 'minimum', 'people', 'finite', 'infinite', 'occurring', 'finite', 'occur', 'defining', 'symmetry', 'line', 'estimator', 'throws', 'line', 'through', 'rolled', 'equal', 'dice', 'bet', 'different', 'based', 'empirical', 'toss', 'tail', 'tosses', 'minimum', 'tosses', 'distinct', 'average', 'tosses', 'large', 'finite', 'pennies', 'total', 'smallest', 'pennies', 'expected', 'real', 'kolmogorov', 'despite', 'apparent', 'rational', 'solving', 'mistakes', 'despite', 'apparent', 'fixed', 'distribution', 'tosses', 'stationary', 'limited', 'index', 'finite', 'indeed', 'specific', 'picked', 'generator', 'random', 'generator', 'random', 'random', 'seed', 'discrepancy', 'discrepancy', 'riffle', 'eigenvalue', 'range', 'reversing', 'net', 'expected', 'random', 'using', 'initial', 'pseudorandom', 'pseudorandom', 'random', 'random', 'seed', 'star', 'distribution', 'absolutely', 'multivariate', 'parker', 'unfoldings', 'solid', 'directed', 'truly', 'ball', 'random', 'sphere', 'prefix', 'type', 'random', 'generated', 'pseudorandom', 'random', 'quasirandom', 'random', 'quasirandom', 'useful', 'quasirandom', 'random', 'pseudorandom', 'pseudorandom', 'quasi', 'random', 'quasirandom', 'computed', 'huge', 'hammersley', 'pseudorandom', 'quasirandom', 'quasirandom', 'random', 'random', 'uniform', 'random', 'statistical', 'specified', 'prime', 'theory', 'expected', 'real', 'function', 'expected', 'length', 'expected', 'complex', 'complex', 'random', 'random', 'chance', 'reproduces', 'required', 'computer-generated', 'pseudorandom', 'term', 'transformed', 'two-dimensional', 'one', 'common', 'simplest', 'random', 'generator', 'random', 'initial', 'starting', 'generated', 'over', 'random', 'random', 'bays', 'random', 'generator', 'real', 'probability', 'principle', 'random', 'random', 'principle', 'pseudorandom', 'random', 'random', 'random', 'random', 'initial', 'starting', 'generating', 'bays', 'discrepancy', 'anderson', 'deterministic', 'index', 'halton', 'interval', 'equal', 'dimension', 'drawbacks', 'quasirandom', 'matrix', 'further', 'eigenvalue', 'minimum', 'transpositions', 'motion', 'unique', 'almost', 'normal', 'left', 'right', 'mean', 'mean', 'traveled', 'probable', 'sign', 'arise', 'catalan', 'point', 'point', 'discrete', 'directions', 'only', 'paths', 'step', 'paths', 'a007764', 'sequence', 'over', 'same', 'paths', 'counting', 'paths', 'random', 'property', 'self-avoiding', 'equal', 'value', 'reasonable', 'noisy', 'fitting', 'unknown', 'worsen', 'free', 'question', 'equal', 'equal', 'function', 'oeis', 'feller', 'expected', 'expected', 'tail', 'expected', 'schilling', 'possible', 'object', 'fixed', 'expected', 'noncontiguous', 'count', 'clumps', 'eulerian', 'hypergeometric', 'element', 'a086266', 'mean', 'oeis', 'total', 'total', 'series', 'successes', 'single', 'several', 'price', 'index', 'statistical', 'data', 'data', 'function', 'data', 'other', 'fall', 'discrete', 'count', 'data', 'dot', 'high', 'distribution', 'data', 'plotting', 'members', 'above', 'histogram', 'bin', 'bin', 'value', 'distribution', 'anova', 'account', 'represent', 'science', 'articles', 'successes', 'account', 'uncorrelated', 'time', 'developed', 'constructed', 'time', 'event', 'satisfying', 'population', 'trial', 'probability', 'successes', 'sampling', 'members', 'function', 'tries', 'size', 'sample', 'members', 'subnormal', 'subnormal', 'dropping', 'distribution', 'even', 'odd', 'parameter', 'large', 'large', 'human', 'normal', 'function', 'random', 'rectangle', 'expected', 'expected', 'uniform', 'expected', 'first', 'expected', 'sum', 'expected', 'first', 'expected', 'sum', 'fixed', 'distribution', 'variate', 'distribution', 'successes', 'distribution', 'distribution', 'expected', 'containing', 'grains', 'divided', 'evenly-spaced', 'slots', 'distribution', 'distribution', 'coin', 'oeis', 'even', 'difference', 'arise', 'total', 'successful', 'table', 'expected', 'successes', 'leading', 'second', 'distribution', 'galaxies', 'change', 'limit', 'zipf', 'equal', 'distribution', 'distributed', 'random', 'random', 'generator', 'mean', 'cars', 'variance', 'occur', 'greater', 'evans', 'idea', 'limit', 'weak', 'limit', 'strong', 'pair', 'sequence', 'limit', 'law', 'strong', 'probability', 'limit', 'strong')
points	('data', 'fall')
fall	('points', 'within', 'bin', 'actually', 'class', 'below', 'times', 'value', 'range', 'value', 'range', 'within', 'distribution', 'within', 'line', 'rest', 'within', 'approximately', 'value', 'number', 'lattice', 'single', 'within', 'centered', 'vertically')
within	('fall', 'falling', 'pair', 'fall', 'standard', 'mean', 'interval', 'fall', 'small', 'number', 'uncertainty', 'birthday', 'day', 'match', 'days', 'entirely', 'one', 'outcome', 'interval', 'fall', 'other', 'lie', 'specified', 'respectively', 'framework', 'graphed', 'additive', 'falling', 'one', 'outlier', 'observation', 'factor', 'observation', 'factor', 'observation', 'factor', 'freedom', 'hypothesis', 'fall', 'interval', 'mean', 'distance')
class	('frequency', 'conjugacy', 'statistics', 'grouping', 'value', 'value', 'interval', 'middle', 'interval', 'set', 'interval', 'frequency', 'descriptive', 'characteristic', 'characteristic', 'boundaries', 'boundaries', 'group', 'method', 'interval', 'interval', 'limit', 'mark', 'mark', 'number', 'conjugacy', 'frequency', 'number', 'set', 'set', 'rounding', 'example', 'fall', 'boundaries', 'p', 'boundaries', 'statistics', 'ends', 'interval', 'interval', 'interval', 'mark', 'interval', 'bin', 'boundaries', 'boundaries', 'limit', 'mark', 'specify', 'interval', 'statistics', 'boundaries', 'boundaries', 'interval', 'value', 'limit', 'mark', 'denoted', 'mark', 'statistics', 'interval', 'interval', 'number', 'boundary', 'frequency', 'interval', 'pair', 'below', 'interval', 'frequency', 'cumulative', 'frequency', 'boundaries', 'specified', 'frequencies', 'frequencies', 'mark', 'taken', 'interval', 'follow', 'moment', 'distribution', 'bin', 'interval', 'wider', 'inequalities', 'algorithm', 'random', 'discrepancy', 'discrete', 'discrepancy', 'subintervals', 'formal', 'upper', 'boundary', 'frequency', 'interval', 'apart', 'bin', 'bin', 'interval', 'calculate', 'distribution', 'probability')
frequency	('class', 'absolute', 'descriptive', 'cumulative', 'cumulative', 'distribution', 'relative', 'relative', 'cumulative', 'computation', 'relative', 'cumulative', 'relative', 'class', 'class', 'distribution', 'data', 'two-way', 'term', 'observed', 'two', 'expected', 'cell', 'expected', 'comparing', 'observed', 'performing', 'expected', 'least', 'probability', 'distribution', 'cumulative', 'upper', 'interval', 'absolute', 'cumulative', 'descriptive', 'absolute', 'class', 'cumulative', 'polygon', 'polygon', 'distribution', 'cumulative', 'relative', 'relative', 'quantile', 'expected', 'statistical', 'table', 'distribution', 'relative', 'cumulative', 'relative', 'cumulative', 'distribution', 'absolute', 'class', 'cumulative', 'class', 'relative', 'relative', 'cumulative', 'distribution', 'polygon', 'statistics', 'curve', 'curve', 'distribution', 'sample', 'kenney', 'cumulative', 'cumulative', 'descriptive', 'absolute', 'cumulative', 'cumulative', 'cumulative', 'distribution', 'relative', 'total', 'point', 'relative', 'descriptive', 'absolute', 'cumulative', 'cumulative', 'cumulative', 'distribution', 'cumulative', 'law', 'word', 'measure', 'use', 'cumulative', 'against', 'cumulative', 'cumulative', 'cumulative', 'polygon', 'absolute', 'class', 'interval', 'distribution', 'distribution', 'polygon', 'cumulative', 'relative', 'relative', 'computed', 'distribution', 'large', 'curve', 'plot', 'distribution', 'distribution', 'polygon', 'plot', 'curve', 'curve', 'distribution', 'distribution', 'polygon', 'cumulative', 'plot', 'polygon', 'cumulative', 'normalized', 'cumulative', 'true', 'signal-to-noise', 'cumulative', 'cumulative', 'probability')
absolute	('distribution', 'frequency', 'mark', 'cumulative', 'total', 'frequency', 'statistics', 'frequency', 'mark', 'cumulative', 'statistics', 'frequency', 'mean', 'deviation', 'statistic', 'frequency', 'ratio', 'statistic', 'frequency', 'statistic', 'deviation', 'deviation', 'statistic', 'deviation', 'value', 'taken', 'error', 'error', 'sum', 'error', 'error', 'error', 'accuracy', 'analysis', 'error', 'error', 'analysis', 'deviation', 'average', 'deviation', 'analysis', 'error', 'formula', 'error', 'analysis', 'error', 'analysis', 'error', 'error', 'analysis', 'error', 'error', 'analysis', 'error', 'error', 'quantities', 'deviation', 'deviation', 'deviation', 'moment', 'point', 'moment', 'average', 'deviation', 'moment', 'deviation', 'deviation', 'moment', 'moment', 'mean', 'mean', 'introduction', 'value', 'sum', 'mean', 'mean', 'moment', 'deviation', 'moment', 'moment', 'moment', 'moment', 'moment', 'deviation', 'deviation', 'largest', 'value', 'distance', 'step', 'offset', 'use', 'value', 'because', 'value', 'plot', 'frequency', 'function', 'value', 'time', 'difference')
descriptive	('frequency', 'statistics', 'value', 'statistics', 'surely', 'statistics', 'number', 'statistics', 'batch', 'statistics', 'law', 'statistics', 'bimodal', 'statistics', 'distribution', 'statistics', 'bin', 'statistics', 'skewness', 'statistics', 'clarity', 'statistics', 'class', 'statistics', 'boundaries', 'statistics', 'interval', 'statistics', 'limit', 'statistics', 'mark', 'statistics', 'frequency', 'statistics', 'level', 'statistics', 'out', 'statistics', 'fence', 'statistics', 'matrix', 'statistics', 'distribution', 'statistics', 'polygon', 'statistics', 'maximum', 'statistics', 'inequality', 'statistics', 'coefficient', 'statistics', 'spread', 'mark', 'hinge', 'hinge', 'range', 'coefficient', 'curve', 'deviation', 'multimodal', 'percentile', 'position', 'population', 'quantile', 'quartile', 'deviation', 'coefficient', 'setting', 'mean', 'frequency', 'frequency', 'mean', 'maximum', 'deviation', 'depth', 'statistical', 'dispersion', 'range', 'step', 'tail', 'trimodal', 'statistic', 'unimodal', 'law', 'useful', 'devices', 'important', 'statistic', 'mean')
statistics	('descriptive', 'cumulative', 'descriptive', 'descriptive', 'lebesgue', 'descriptive', 'anomalous', 'descriptive', 'descriptive', 'logarithmic', 'descriptive', 'bimodal', 'descriptive', 'bimodal', 'descriptive', 'bin', 'descriptive', 'interquartile', 'descriptive', 'class', 'descriptive', 'characteristic', 'descriptive', 'class', 'descriptive', 'bin', 'descriptive', 'class', 'descriptive', 'class', 'present', 'contingency', 'sample', 'variable', 'descriptive', 'absolute', 'factor', 'descriptive', 'descriptive', 'fence', 'descriptive', 'adjacent', 'descriptive', 'fisher', 'descriptive', 'absolute', 'descriptive', 'frequency', 'descriptive', 'apodization', 'descriptive', 'descriptive', 'lorenz')
cumulative	('statistics', 'count', 'count', 'frequency', 'frequency', 'relative', 'frequency', 'frequency', 'absolute', 'relative', 'denoted', 'frequency', 'denoted', 'frequency', 'interval', 'count', 'count', 'frequency', 'relative', 'frequency', 'frequency', 'absolute', 'relative', 'frequency', 'class', 'count', 'count', 'frequency', 'relative', 'frequency', 'function', 'proportion', 'onto', 'proportion', 'expressed', 'distribution', 'say', 'say', 'estimated', 'proportion', 'frequency', 'relative', 'frequency', 'frequency', 'frequency', 'frequency', 'frequency', 'frequency', 'frequency', 'relative', 'frequency', 'function', 'value', 'function', 'distribution', 'distribution', 'plot', 'frequency', 'continuous', 'frequency', 'including', 'frequency', 'ogive', 'frequency', 'relative', 'frequency', 'continuous', 'frequency', 'showing', 'sample', 'density', 'calculate', 'frequency', 'calculate', 'frequency', 'expected', 'analysis', 'sum', 'distribution', 'distribution', 'function', 'distribution', 'function', 'distribution', 'distribution', 'distribution', 'function', 'distribution', 'density', 'distribution', 'probability', 'normalized', 'distribution', 'form', 'normal', 'probability', 'distribution', 'student', 'distribution', 'function', 'distribution', 'function', 'distribution', 'function', 'distribution', 'cdf', 'frequency', 'distribution', 'count', 'count', 'frequency', 'describing', 'probability', 'function', 'distribution', 'limiting', 'distribution')
count	('cumulative', 'cumulative', 'cumulative', 'cumulative', 'cumulative', 'cumulative', 'difference', 'number', 'inversion', 'cramer', 'value', 'number', 'various', 'cluster', 'per', 'run', 'per', 'plot', 'number', 'cumulative', 'cumulative')
value	('nearest', 'adjacent', 'descriptive', 'similar', 'data', 'slight', 'data', 'class', 'class', 'actually', 'specify', 'class', 'central', 'kenney', 'useful', 'know', 'computing', 'one', 'less', 'one', 'two', 'outside', 'adjacent', 'discrete', 'following', 'minimum', 'high-water', 'running', 'oeis', 'bottom', 'single', 'percentile', 'say', 'below', 'function', 'th', 'th', 'say', 'q2', 'running', 'running', 'expectation', 'fisher', 'function', 'symmetric', 'tends', 'less', 'inferred', 'quantity', 'actual', 'absolute', 'true', 'fall', 'true', 'fall', 'returned', 'alpha', 'erf', 'p', 'significance', 'true', 'quantity', 'inferred', 'relative', 'expectation', 'polyache', 'expectation', 'function', 'expectation', 'satisfies', 'expectation', 'satisfies', 'expectation', 'expected', 'expectation', 'kenney', 'finding', 'one', 'estimator', 'parameter', 'first', 'expected', 'observed', 'sum', 'expectation', 'expectation', 'wald', 'expectation', 'sum', 'sequence', 'stochastic', 'sample', 'central', 'respective', 'harmonic', 'arithmetic', 'notation', 'absolute', 'analytical', 'moment-generating', 'raw', 'discrete', 'namely', 'possible', 'need', 'denotes', 'bias-corrected', 'expected', 'sample', 'noting', 'already', 'extreme', 'sample', 'variate', 'producing', 'discrete', 'population', 'multivariate', 'equally', 'extreme', 'distribution', 'add', 'people', 'solving', 'simpler', 'expectation', 'limit', 'domain', 'sent', 'notion', 'th', 'prove', 'oeis', 'variate', 'greater', 'observed', 'strictly', 'p', 'probability', 'alpha', 'hypothesis', 'cumulative', 'integral', 'take', 'attained', 'domain', 'expectation', 'gain', 'p', 'population', 'p', 'point', 'assumed', 'two-element', 'red', 'oeis', 'iterating', 'oeis', 'take', 'assumes', 'denoted', 'function', 'berestycki', 'zero', 'montroll', 'expectation', 'absolute', 'oeis', 'expectation', 'root-mean-square', 'oeis', 'statistic', 'specifically', 'equal', 'greater', 'odd', 'even', 'number', 'list', 'two', 'variable', 'different', 'set', 'see', 'sum', 'because', 'absolute', 'results', 'fit', 'order', 'absolute', 'function', 'based', 'merit', 'smallest', 'producing', 'smallest', 'merit', 'variable', 'function', 'best', 'close', 'sum', 'partial', 'numerical', 'th', 'same', 'count', 'cluster', 'mean', 'expected', 'kenney', 'period', 'period', 'sort', 'inflation', 'period', 'period', 'difference', 'draw', 'identifying', 'closest', 'generated', 'fall', 'letter', 'letter', 'display', 'set', 'alpha', 'number', 'alpha', 'statistical', 'p', 'significance', 'appropriate', 'entire', 'comparison', 'experiment-wide', 'critical', 'equation', 'alpha', 'hypothesis', 'assumes', 'greater', 'measured', 'subtleties', 'parameter', 'calculating', 'significance', 'alpha', 'observed', 'alpha', 'alternative', 'p', 'paired', 'fact', 'sample', 'critical', 'chi-squared', 'paired', 'predictive', 'probability', 'predictive', 'probability', 'predictive', 'statistical', 'due', 'variate', 'greater', 'observed', 'strictly', 'one', 'alpha', 'coincidence', 'p', 'probable', 'significance', 'statistical', 'alpha', 'predictive', 'sensitivity', 'appropriate', 'predictive', 'sensitivity', 'time', 'weakly', 'prediction', 'one', 'ranging', 'abramowitz', 'extreme', 'distribution', 'extreme', 'distribution', 'extreme', 'extreme', 'distribution', 'distribution', 'extreme', 'extreme', 'distribution', 'extreme', 'distribution', 'extreme', 'extreme', 'distribution', 'distribution', 'extreme', 'distribution', 'assumes', 'interval', 'variate', 'integral', 'assumes', 'range', 'assumes', 'range', 'feller', 'approximation', 'approximation', 'a001147', 'intermediate', 'approximation', 'probable', 'expected', 'random', 'observed', 'probable', 'error', 'oeis', 'population', 'least', 'initial', 'problem', 'absolute', 'probable', 'modified', 'distribution', 'observed', 'purely', 'oeis', 'extreme', 'distribution', 'estimator', 'oeis', 'expanding', 'abramowitz', 'oeis', 'probable', 'expectation', 'expectation', 'generating', 'expectation', 'computed', 'possible', 'represented', 'poisson', 'variate', 'less', 'distributed', 'trial', 'finding', 'distribution', 'memoryless', 'take', 'probability', 'numerical', 'due', 'probability', 'occur', 'probability', 'probability', 'smaller', 'variate', 'greater', 'goes', 'restricted')
nearest	('value', 'still', 'denotes', 'integer', 'bit', 'integer', 'midpoint', 'line')
still	('nearest', 'inside', 'easier', 'augmenting', 'zhu', 'other', 'described', 'hawkes', 'player', 'come', 'money', 'come', 'point', 'trend', 'great', 'outset', 'use', 'normal', 'acceptable', 'closest', 'inside')
inside	('still', 'inner', 'still', 'inner')
inner	('inside', 'hinges', 'square', 'integral', 'outside', 'under', 'inside', 'a050996', 'integral')
fence	('adjacent', 'far', 'statistics', 'tukey', 'far', 'out', 'descriptive', 'statistic', 'h', 'box')
adjacent	('fence', 'value', 'statistics', 'value', 'connecting', 'group', 'horizontally', 'crossbars', 'set', 'circular')
event	('probability', 'lebesgue', 'probability', 'occurrence', 'number', 'extreme', 'likely', 'phenomenon', 'reflects', 'markov', 'intersection', 'written', 'inclusion-exclusion', 'occurring', 'distribution', 'consisting', 'probability', 'perceived', 'extremely', 'expected', 'expected', 'space', 'happen', 'first', 'second', 'happen', 'first', 'independence', 'probability', 'already', 'likelihood', 'mark', 'never', 'difference', 'different', 'th', 'denoted', 'th', 'never', 'one', 'occur', 'occur', 'mutually', 'conditional', 'probability', 'ways', 'occur', 'compared', 'occur', 'together', 'particular', 'set', 'occur', 'governed', 'very', 'sample', 'probability', 'mutually', 'set', 'random', 'space', 'space', 'place', 'occurred', 'spatial-temporal', 'occurring', 'tail', 'occur', 'themselves', 'probabilities', 'conditional', 'real', 'probability', 'occurring', 'probability', 'certain', 'assumed', 'p', 'mutually', 'outcome', 'number', 'assigned', 'experiment', 'trial', 'outcome', 'independent', 'trial', 'independent', 'trial', 'experiment', 'trial', 'experiment', 'poisson', 'complete', 'poisson', 'poisson', 'poisson', 'differentiating', 'probability', 'probability', 'littlewood', 'one', 'year')
lebesgue	('event', 'statistics', 'measure', 'relative', 'denotes', 'measure', 'ordinary')
measure	('almost', 'lebesgue', 'ratio', 'size', 'size', 'curve', 'inequality', 'degree', 'provide', 'strength', 'regarded', 'provide', 'statistics`descriptivestatistics`', 'suggested', 'skewness', 'degree', 'encountered', 'average', 'accuracy', 'spearman', 'strength', 'r-estimate', 'monotone', 'relative', 'lebesgue', 'pawlas', 'intensity', 'point', 'intensity', 'point', 'intensity', 'intimately', 'intensity', 'time', 'probability', 'frequency', 'probability', 'probability', 'probability', 'space', 'probability', 'probability', 'radon', 'state', 'probability', 'space', 'probability', 'probability', 'probability', 'random', 'discrepancy', 'deviation', 'wiener', 'random', 'wiener', 'agreement', 'quantity', 'deviation', 'criteria', 'typically', 'mentioned', 'distribution', 'setting', 'radon', 'space', 'probability', 'probability')
almost	('measure', 'surely', 'distribution', 'statistic', 'spp', 'finite', 'sure', 'distribution', 'continuous', 'number', 'continuous', 'differentiable', 'etc', 'always', 'etc', 'always', 'gardner', 'always')
surely	('almost', 'descriptive', 'increasing', 'above')
anomalous	('number', 'statistics', 'cancellation', 'out', 'third')
cancellation	('anomalous', 'benford')
benford	('cancellation', 'law', 'phenomenon', 'law', 'out', 'law', 'newcomb', 'law', 'hill', 'law', 'numb3rs', 'law', 'close', 'below', 'law', 'fact', 'law', 'example', 'law', 'compiled', 'original', 'following', 'law', 'a055442', 'law', 'arising', 'distribution', 'law')
law	('benford', 'phenomenological', 'first', 'first', 'benford', 'benford', 'benford', 'unquestionably', 'benford', 'character', 'benford', 'applies', 'physics', 'many', 'benford', 'applies', 'benford', 'benford', 'million', 'benford', 'using', 'benford', 'descriptive', 'up', 'breaks', 'goetz', 'frequency', 'zipf', 'descriptive', 'problem', 'truly', 'common', 'circular', 'random', 'semicircle', 'considers', 'large', 'circular', 'integer', 'semicircle', 'common', 'wigner', 'first', 'semicircle', 'exception', 'semicircle', 'random', 'circular', 'random', 'satisfies', 'large', 'statistic', 'large', 'probability', 'space', 'zipf', 'explicitly', 'power', 'manova', 'power', 'power', 'power', 'regression', 'weak', 'large', 'logarithmic', 'benford', 'log', 'exponential', 'weak', 'large', 'zipf', 'zero', 'large', 'strong', 'large', 'weak', 'large', 'mosteller', 'truly', 'strong', 'large', 'strong', 'small', 'strong', 'large', 'strong', 'large', 'strong', 'large', 'arithmetic', 'large', 'number', 'truly', 'strong', 'small', 'weak', 'large', 'strong', 'large', 'weak', 'large', 'arithmetic', 'truly', 'strong', 'large')
similar	('value', 'meaning', 'size', 'function', 'distribution', 'sum', 'different', 't', 'fisher', 'definition', 'definition', 'function', 'form', 'distribution', 'binomial')
meaning	('similar', 'mathematics', 'particular', 'close', 'accuracy', 'true', 'accuracy', 'true', 'dist', 'topology', 'set', 'what', 'technical', 'generalization', 'mathematics')
manner	('batch', 'correlated', 'next', 'correlated', 'next')
batch	('manner', 'descriptive')
phenomenological	('law',)
first	('law', 'digit', 'law', 'digit', 'noting', 'pages', 'probability', 'distribution', 'digits', 'distribution', 'digit', 'version', 'table', 'continuous', 'second', 'noting', 'measurement', 'lower', 'contributes', 'denoting', 'third', 'below', 'members', 'quartile', 'identical', 'third', 'position', 'third', 'third', 'third', 'polynomial', 'kind', 'p', 'size', 'sample', 'variance', 'unbiased', 'mean', 'sample', 'value', 'sample', 'p', 'central', 'cumulant', 'integral', 'duck', 'aim', 'hausdorff', 'obtain', 'pearson', 'skewness', 'function', 'raw', 'p', 'obtain', 'notation', 'variance', 'sample', 'working', 'working', 'term', 'finite', 'two', 'interval', 'sample', 'standardized', 'student', 'obtain', 'different', 'two', 'problem', 'solved', 'problem', 'posed', 'htt', 'p', 'probability', 'event', 'happen', 'event', 'independently', 'opined', 'outcome', 'principle', 'enunciated', 'probability', 'duelist', 'game', 'proposed', 'before', 'turns', 'up', '$8', 'player', 'wins', 'homogeneous', 'order', 'duck', 'aim', 'small', 'term', 'type', 'one', 'presentations', 'lie', 'half', 'edelman', 'law', 'observed', 'ill-behaved', 'integral', 'function', 'integral', 'theorem', 'term', 'origin', 'step', 'origin', 'step', 'before', 'down', 'table', 'denoted', 'coefficient', 'sum', 'line', 'degree', 'transpose', 'polynomial', 'digit', 'single', 'one', 'wallace', 'done', 'performing', 'hypothesis', 'part', 'outcome', 'comparison', 'function', 'corrected', 'freedom', 'th', 'kind', 'cumulant', 'moment-generating', 'moment', 'subfactorial', 'oeis', 'large', 'distribution', 'moment', 'central', 'function', 'raw', 'moment', 'central', 'kind', 'using', 'moment', 'central', 'moment', 'papoulis', 'function', 'analytically', 'analytically', 'central', 'analytically', 'raw', 'moment', 'central', 'function', 'moment', 'th', 'function', 'p', 'second', 'function', 'central', 'function', 'moment', 'central', 'excess', 'function', 'analytically', 'explicitly', 'analytically', 'explicitly', 'taken', 'number', 'expected', 'sum', 'case', 'number', 'following', 'sum', 'integer', 'function', 'before', 'n', 'raw', 'excess', 'factorial', 'solution', 'function', 'explicitly', 'transcendent', 'explicitly', 'formula', 'raw', 'function', 'written')
digit	('first', 'first', 'leading', 'tends', 'one', 'out', 'decimal', 'logarithmic', 'data', 'first', 'mantissa', 'accuracy', 'variance', 'perform', 'many', 'significant', 'express', 'error', 'prove', 'computer', 'single', 'pair', 'different', 'different', 'pair', 'preceding', 'single', 'first', 'certainly', 'final', 'column')
phenomenon	('leading', 'benford', 'statistical', 'stating', 'event', 'appears', 'walk', 'brownian', 'sample', 'sampling', 'waveform')
leading	('phenomenon', 'digit', 'component', 'set', 'included', 'triangular', 'number', 'transcendental')
listings	('tables',)
tables	('listings', 'examining')
tends	('digit', 'occur', 'size', 'value', 'fact', 'increase', 'increases', 'decrease')
occur	('tends', 'mark', 'independent', 'outliers', 'comparing', 'sequence', 'running', 'number', 'borel', 'ttt', 'either', 'tail', 'tosses', 'tail', 'tosses', 'length', 'subsequences', 'expected', 'around', 'definition', 'event', 'ways', 'second', 'independently', 'event', 'event', 'no', 'one', 'preferentially', 'event', 'equally', 'event', 'expressed', 'event', 'variate', 'paths', 'tail', 'tosses', 'probability', 'binomial', 'because', 'outcome', 'number', 'value', 'probability', 'smaller', 'distribution')
greater	('probability', 'expected', 'stating', 'deviation', 'mean', 'probability', 'tile', 'coin', 'gamble', 'chance', 'value', 'equal', 'less', 'value', 'fit', 'value', 'measured', 'equal', 'deviation', 'd-statistic', 'critical', 'value', 'equal', 'variate', 'sum', 'value', 'number')
expected	('greater', 'one', 'know', 'frequency', 'cell', 'number', 'computing', 'frequencies', 'cell', 'frequency', 'frequencies', 'frequency', 'frequency', 'variable', 'number', 'value', 'moment', 'value', 'mean', 'value', 'similarly', 'stake', 'loss', 'reduces', 'property', 'wait', 'less', 'wait', 'event', 'take', 'event', 'occur', 'set', 'number', 'denotes', 'throw', 'large', 'number', 'present', 'bunching', 'distribution', 'number', 'number', 'real', 'multiplying', 'number', 'head', 'number', 'tail', 'number', 'continuing', 'number', 'longest', 'run', 'bloom', 'number', 'differ', 'value', 'observed', 'cumulative', 'distribution', 'function', 'value', 'simplifies', 'continuous', 'interestingly', 'number', 'number', 'a001048', 'number', 'first', 'number', 'a090138', 'number', 'summarizes', 'number', 'considers', 'number', 'function', 'number', 'poisson', 'difference', 'actual')
one	('expected', 'digit', 'matthews', 'striking', 'farber', 'benefit', 'table', 'easily', 'example', 'useful', 'value', 'expect', 'whereby', 'deduce', 'application', 'major', 'value', 'maximum', 'infinite', 'except', 'size', 'distribution', 'mode', 'possessing', 'unimodal', 'two', 'bimodal', 'three', 'four', 'integrates', 'over', 'formulation', 'easily', 'stored', 'processor', 'bits', 'word', 'deviation', 'value', 'identically', 'zero', 'kurtosis', 'infinite', 'hunting', 'sees', 'statisticians', 'high', 'multivariate', 'processes', 'intensity-based', 'independent', 'equivalent', 'processes', 'example', 'processes', 'whereby', 'multivariate', 'opposed', 'involving', 'least', 'least', 'within', 'triangles', 'needle', 'shorter', 'needle', 'longer', 'least', 'line', 'above', 'million', 'analysis', 'accurate', 'intersect', 'bet', 'least', 'four', 'least', 'double-six', 'least', 'double-six', 'domain', 'domain', 'over', 'player', 'player', 'flip', 'pennies', 'process', 'player', 'two', 'player', 'connected', 'oft-discussed', 'difference', 'multidimensional', 'event', 'occurrence', 'precludes', 'least', 'six', 'six', 'believe', 'occur', 'subject', 'several', 'range', 'defines', 'difference', 'multidimensional', 'chance', 'six', 'themselves', 'least', 'acquaintance', 'hunting', 'statistician', 'high', 'dürer', 'first', 'done', 'overlap', 'concave', 'cited', 'catherine', 'probability', 'oeis', 'number', 'similarly', 'divide', 'large', 'start', 'stochastic', 'toward', 'other', 'walk', 'dimension', 'again', 'pelya', 'path', 'point', 'grid', 'corner', 'cevian', 'vertices', 'length', 'first', 'length', 'adding', 'essentially', 'less', 'sequence', 'consecutive', 'object', 'type', 'within', 'categories', 'microarrays', 'motivating', 'assigned', 'possible', 'curve', 'above', 'disk', 'calculate', 'probabilities', 'case', 'fisher', 'issue', 'math', 'significant', 'observed', 'reject', 'model', 'fewer', 'value', 'denoted', 'least', 'pair', 'value', 'particular', 'out', 'labeled', 'two', 'satisfies', 'three', 'time', 'hit', 'change', 'probability', 'change', 'distribution', 'starting', 'outer', 'large', 'several', 'event', 'million')
out	('digit', 'benford', 'far', 'descriptive', 'fence', 'fraction', 'writing', 'shape', 'written', 'explicitly', 'statisticians', 'hunting', 'turns', 'quantity', 'singled', 'anomalous', 'people', 'group', 'birthdays', 'equally', 'people', 'group', 'people', 'group', 'days', 'possible', 'start', 'total', 'starting', 'smallest', 'starting', 'most', 'come', 'ahead', 'pointed', 'variety', 'pointed', 'detailed', 'come', 'ahead', 'come', 'ahead', 'statistician', 'hunting', 'great', 'shuffle', 'shuffle', 'step', 'only', 'arbitrary', 'alternative', 'one', 'set', 'successes', 'bernoulli', 'successes', 'bernoulli', 'successes', 'selection', 'total', 'probability', 'dropped', 'probability')
instance	('examining', 'chi-squared', 'bland-altman', 'eyebrow')
examining	('instance', 'tables', 'analyzed', 'noise')
logarithms	('noting',)
noting	('logarithms', 'first', 'worth', 'above-mentioned', 'seen', 'first', 'table', 'identity', 'begin', 'value', 'precisely', 'derived', 'probability', 'fact', 'probability', 'proceed', 'characteristic', 'demonstrated', 'probability')
pages	('first', 'worn', 'later', 'newcomb')
worn	('pages', 'smudged')
smudged	('worn', 'later')
later	('smudged', 'pages')
newcomb	('pages', 'benford')
unquestionably	('law', 'applies')
applies	('unquestionably', 'many', 'law', 'data', 'law', 'only', 'function', 'variable')
many	('applies', 'situations', 'law', 'powers', 'word', 'specialized', 'use', 'digit', 'programming', 'offers', 'advantages', 'confusingly', 'distribution', 'opposed', 'processes', 'notions', 'involving', 'bivariate', 'getting', 's', 's', 'place', 'little', 'mistakes', 'mistakes', 'bet', 'matter', 'tosses', 'role', 'aspects', 'possible', 'possible', 'observation', 'experts', 'different', 'distribution', 'convenient', 'distribution', 'common', 'end', 'approximating', 'central', 'noncentral', 'influenced', 'small')
situations	('many', 'real', 'optimal', 'everitt', 'distribution')
real	('situations', 'million', 'constants', 'matrix', 'function', 'set', 'state', 'number', 'imbalance', 'location', 'arbitrary', 'random', 'along', 'matrix', 'number', 'probability', 'expected', 'gaussian', 'random', 'eigenvalue', 'matrix', 'random', 'symmetric', 'matrices', 'sequence', 'matrix', 'variable', 'event', 'number', 'symmetric', 'interval', 'wigner', 'large', 'symmetric', 'spherical', 'sample', 'observation', 'effect', 'observation', 'effect', 'observation', 'substitution', 'line', 'properties', 'spectra', 'data', 'distribution')
world	('satisfactory', 'small', 'problem', 'small', 'problem', 'small', 'problem', 'small', 'network', 'alone')
satisfactory	('world', 'explanation')
explanation	('satisfactory', 'been')
been	('explanation', 'only', "they've", 'assumed', 'zero', 'shown', 'observation', 'grouped', 'assumptions', 'optimize', 'computation', 'done', 'data', 'years', 'attempt', 'experimentally', 'prediction', 'confirmed', 'edge', 'computed', 'objects', 'picked', 'though', 'amazingly', 'proven', 'slade', 'conjectured', 'slade', 'conjectured', 'data', 'neither', 'probabilities', 'believe', 'established', 'equation', 'generalized', 'use', 'identity', 'distribution', 'saslaw', 'yet', 'proven', 'disproven')
only	('been', 'recently', 'applies', 'scale-invariant', 'quantities', 'keeps', 'significant', 'significant', 'distribution', 'papoulis', 'involving', 'last', 'precomputed', 'running', 'remains', 'find', 'process', 'difference', 'using', 'very', 'information', 'signs', 'due', 'imprecise', 'head', 'time', 'lose', 'bet', 'procedure', 'done', 'artifice', 'step', 'allowed', 'number', 'restricted', 'composed', 'horizontal', 'recurrence', 'fixed', 'affect', 'agreement', 'whisker', 'out', 'distribution', 'take', 'discrete', 'board', 'nails', 'distribution', 'satisfies', 'memoryless')
recently	('only', 'through')
through	('recently', 'work', 'dividing', 'rearranging', 'runs', 'property', 'five', 'dividing', 'statistic', 'definition', 'up', 'th', 'number', 'three', 'identified', 'statistical', 'line', 'set', 'operations', 'premultiplication', 'operations', 'postmultiplication', 'line', 'set', 'fit', 'population')
work	('through', 'hill', 'simpler', '◇', 'second', 'quantity', 'statistical', 'bit', 'discrete', 'space', 'daley', 'term', 'distribution', 'reserves', 'form')
hill	('work', 'benford', 'distribution', 'rigorously')
character	('law', 'charlie', 'charles')
charlie	('character', 'eppes', 'genius', 'eppes')
eppes	('charlie', 'analogy', 'charlie', 'runs', 'charles', 'amita')
analogy	('eppes', 'help', 'p')
help	('analogy', 'solve')
solve	('help', 'series', 'unit', 'equation', 'interval', 'desire', 'technique', 'overdetermined', 'expression', 'find')
series	('solve', 'high', 'harmonic', 'statistical', 'finite', 'characteristic', 'raw', 'side', 'characteristic', 'time', 'time', 'analysis', 'independent', 'tosses', 'time', 'analysis', 'time', 'analysis', 'time', 'analysis', 'time', 'analysis', 'time', 'analysis', 'time', 'analysis', 'time', 'analysis', 'time', 'analysis', 'time', 'analysis', 'time', 'analysis', 'time', 'analysis', 'time', 'analysis', 'time', 'analysis', 'time', 'analysis', 'time', 'analysis', 'time', 'analysis', 'time', 'analysis', 'time', 'analysis', 'time', 'analysis', 'time', 'analysis', 'asymptotic', 'top', 'formal', 'edgeworth', 'charlier', 'charlier', 'gram-charlier', 'characteristic', 'formal', 'wallace', 'charlier', 'statistical', 'edgeworth', 'charlier', 'edgeworth', 'edgeworth', 'number', 'binomial', 'normal', 'take', 'edgeworth', 'collecting', 'cramer', 'uniformly', 'edgeworth', 'statistical', 'charlier', 'cornish', 'time', 'decrease', 'time', 'analysis', 'time', 'analysis', 'nonstationary', 'time', 'time', 'time', 'analysis', 'time', 'analysis', 'time', 'analysis', 'time', 'analysis', 'time', 'analysis', 'time', 'analysis', 'time', 'analysis', 'time', 'analysis', 'time', 'analysis', 'time', 'analysis', 'time', 'analysis', 'common', 'time', 'daily', 'time', 'analysis', 'time', 'analysis', 'time', 'analysis', 'time', 'analysis', 'time', 'analysis', 'time', 'analysis', 'time', 'slightly', 'definition', 'log', 'distribution', 'log', 'distribution', 'log', 'distribution', 'asymptotic', 'geometric', 'hypergeometric', 'term', 'expansion', 'log', 'distribution', 'converging', 'expansion')
high	('series', 'burglaries', 'a096618', 'water', 'group', 'low', 'statistic', 'water', 'mark', 'water', 'statistic', 'water', 'distribution', 'peak', 'second', 'one', 'second', 'one', 'integration', 'fact', 'number', 'members', 'low')
burglaries	('high', 'season')
running	('season', 'value', 'sequence', 'maximum', 'maximum', 'value', 'maxima', 'sequence', 'maxima', 'value', 'maximum', 'occur', 'maximum', 'only', 'set', 'average')
dimensionless	('numerical',)
numerical	('dimensionless', 'analytic', 'full', 'language', 'approximate', 'quantities', 'track', 'accuracy', 'end', 'quantity', 'left', 'drawbacks', 'kind', 'value', 'sorted', 'without', 'normalization', 'a086245', 'value', 'convenient')
depend	('data', 'sample', 'programmer', 'variance', 'mean', 'sample', 'population', 'distribution', 'size', 'length', 'distribution', 'distinction', 'argument', 'physical', 'outcome', 'probability')
universal	('unit', 'probability')
invariant	('number', 'under')
under	('invariant', 'change', 'variables', 'area', 'line', 'model', 'group', 'matrix', 'number', 'what', 'cumulant', 'restrictive', 'normal', 'commutative', 'invariance', 'time', 'vector', 'inner', 'medicine', 'completely', 'hypotheses', 'assumption', 'hypothesis', 'rejection', 'assumption', 'significant', 'experiment', 'identical', 'publish', 'image', 'set', 'distribution', 'additional')
change	('under', 'walk', 'reduce', 'group', 'scale', 'rate', 'distribution', 'rate', 'distribution', 'probability', 'rate', 'complete', 'above', 'moment-generating', 'nonoverlapping', 'one', 'sufficiently', 'one', 'number', 'sufficiently')
scale	('normalization', 'distribution', 'matrix', 'linear', 'correlation', 'change', 'affect', 'parameter', 'parameter', 'parameter', 'parameter', 'unit', 'matrix', 'parameter', 'parameter')
normalization	('scale', 'differentiating', 'constrained', 'distribution', 'uniformly', 'log-series', 'numerical', 'factor')
differentiating	('normalization', 'setting', 'event', 'necessarily', 'moment', 'raw')
setting	('differentiating', 'solution', 'record', 'descriptive', 'general', 'locally', 'vector', 'above', 'expectation', 'equal', 'measure', 'probability')
solution	('setting', 'proper', 'closed-form', 'distribution', 'correct', 'laplace', 'reproduced', 'buffon', 'buffon', 'written', 'skew', 'provide', 'problem', 'yield', 'vector', 'least', 'equation', 'square', 'problem', 'limit', 'procedure', 'fit', 'one-parameter', 'using', 'form', 'continuous', 'distribution', 'equation', 'distribution', 'distribution', 'function', 'initial', 'complete', 'first')
proper	('solution', 'probability', 'kurtosis', 'equal', 'denotes', 'manufacturing', 'use')
physics	('law', 'human', 'integral', 'integral', 'normal')
human	('physics', 'convention', 'produce', 'down', 'number')
convention	('human', 'impose', 'literature', 'literature', 'merit', 'tukey', 'usual')
impose	('convention',)
example	('randomly', 'striking', 'benford', 'above', 'data', 'class', 'above', 'probability', 'one', 'sequence', 'data', 'point', 'sequence', 'quantity', 'simple', 'problem', 'quantity', 'sum', 'sample', 'statistical', 'sum', 'sum', 'walk', 'markov', 'transformations', 'characteristic', 'following', 'correctly', 'derive', 'discrete', 'transformations', 'variance', 'log', 'one', 'includes', 'fair', 'probability', 'function', 'normal', 'point', 'sample', 'temporal', 'hammersley', 'either', 'martingale', 'total', 'shown', 'concave', 'subintervals', 'possible', 'box-muller', 'picking', 'ordinary', 'recurrence', 'common', 'wiener', 'kolmogorov-smirnov', 'iteration', 'nonlinear', 'arise', 'list', 'sum', 'application', 'suppose', 'time', 'tossing', 'bernoulli', 'probabilities', 'bivariate', 'normal')
randomly	('example', 'street', 'cards', 'cards', 'results', 'transpositions', 'step', 'taken', 'parked')
street	('randomly', 'addresses')
addresses	('street', 'obey')
obey	('addresses', 'something', 'identities', 'variable', 'probabilistic', 'probabilities', 'certain', 'variable', 'probabilistic', 'semicircle', 'gamma', 'orthogonality', 'strong')
something	('obey', 'close')
close	('something', 'benford', 'meaning', 'ties', 'side', 'very', 'normal', 'value', 'best-fit', 'definition', 'surprising')
powers	('many', 'lie', 'error')
lie	('powers', 'outside', 'interval', 'left', 'closer', 'diameter', 'entirely', 'probability', 'two', 'diameter', 'entirely', 'probability', 'two', 'diameter', 'entirely', 'probability', 'two', 'coin', 'single', 'probability', 'two', 'trial', 'first', 'within', 'eigenvalue', 'interval', 'point', 'solving', 'point', 'roughly')
cutoffs	('probability',)
decimal	('digit', 'significant', 'right', 'point', 'significant', 'binary', 'fact', 'significant', 'right', 'point', 'significant', 'two')
logarithmic	('digit', 'distribution', 'above', 'statistics', 'distribution', 'fitting', 'least', 'fitting', 'least', 'fitting', 'regression', 'fitting', 'distribution', 'distribution', 'function', 'moment-generating', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'law', 'expression', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution')
above	('distribution', 'tabulated', 'function', 'logarithmic', 'histogram', 'example', 'example', 'contingency', 'total', 'table', 'coefficient', 'need', 'number', 'equality', 'axis', 'left', 'figure', 'range', 'third', 'mark', 'sequence', 'using', 'formulation', 'range', 'mean', 'integral', 'term', 'procedure', 'iterating', 'procedure', 'curve', 'varying', 'plotted', 'variance', 'unbiased', 'trial', 'needles', 'plot', 'derived', 'p', 'figure', 'needle', 'one', 'area', 'figure', 'case', 'definition', 'paucity', 'below', 'set', 'various', 'plot', 'integrand', 'initial', 'illustrations', 'polyhedron', 'buekenhout', 'shown', 'basket', 'distribution', 'random', 'plotted', 'complex', 'shown', 'criteria', 'surely', 'definition', 'step', 'position', 'dimension', 'observation', 'correlation', 'setting', 'started', 'procedure', 'constant', 'unsettled', 'plot', 'root', 'polynomial', 'root', 'minimum', 'left', 'length', 'bin', 'plot', 'number', 'histogram', 'one', 'right', 'statisticalplots`', 'data', 'set', 'right', 'mentioned', 'remain', 'plot', 'p', 'distribution', 'distribution', 'change', 'equation', 'symbol', 'plotted', 'plotted', 'plotted', 'coefficient', 'plot', 'precisely', 'central', 'figure', 'variant', 'distribution', 'wolfram', 'mean', 'equation')
tabulated	('above', 'variable')
below	('benford', 'table', 'distribution', 'class', 'equality', 'axis', 'fall', 'line', 'quartile', 'first', 'value', 'quantity', 'variable', 'normal', 'distributed', 'normal', 'above', 'embedded', 'three', 'diagonally', 'plot')
scale-invariant	('only',)
variety	('number', 'different', 'taken', 'different', 'encountered', 'normally', 'out', 'literature', 'together', 'criteria', 'study', 'different')
different	('variety', 'variety', 'number', 'several', 'taken', 'slightly', 'completely', 'number', 'function', 'distribution', 'two', 'similar', 'studied', 'contexts', 'process', 'exciting', 'distinguish', 'multivariate', 'birthday', 'third', 'birthday', 'first', 'number', 'three', 'completely', 'fundamentally', 'idea', 'event', 'type', 'stationarity', 'definition', 'two', 'solids', 'slightly', 'definition', 'gaps', 'several', 'value', 'time', 'digit', 'digit', 'two', 'completely', 'slightly', 'same', 'distribution', 'variety', 'alpha', 'eight', 'lizard', 'pairwise', 'many', 'ways', 'slightly', 'distribution', 'function', 'normal', 'slightly', 'form', 'completely', 'statistical')
sources	('fact', 'table')
fact	('sources', 'rigorous', 'benford', 'reflects', 'probability', 'decimal', 'exact', 'set', 'tends', 'distribution', 'play', 'mean', 'de', 'logic', 'noted', 'ignoring', 'probability', 'noting', 'play', 'refers', 'subintervals', 'pascal', 'functional', 'theorem', 'sum', 'agreement', 'high', 'test', 'value', 'name', 'based')
rigorous	('fact', 'investigation')
investigation	('rigorous', 'central', 'distribution')
central	('investigation', 'midvalue', 'value', 'hinge', 'peak', 'sample', 'moment', 'estimator', 'moment', 'estimator', 'sample', 'moment', 'moment', 'sample', 'sample', 'moment', 'statistic', 'sample', 'moment', 'sample', 'population', 'sample', 'sample', 'moment', 'moment', 'moment', 'sample', 'moment', 'sample', 'underlying', 'sample', 'moment', 'moment', 'moment', 'moment', 'moment', 'limit', 'value', 'first', 'mathstatica', 'mathstatica', 'moment', 'multivariate', 'respectively', 'moment', 'sample', 'moment', 'term', 'moment', 'multivariate', 'statistic', 'moment', 'fourth', 'th', 'moment', 'moment', 'function', 'mean', 'moment', 'mean', 'term', 'moment', 'moment', 'moment', 'moment', 'sample', 'moment', 'population', 'computation', 'th', 'second', 'moment', 'second', 'moment', 'moment', 'second', 'moment', 'moment', 'rule', 'column', 'radius', 'two', 'notation', 'sample', 'sample', 'moment', 'p', 'th', 'similarly', 'function', 'constant', 'analog', 'limit', 'first', 'first', 'first', 'moment', 'first', 'first', 'surprising', 'limit', 'find', 'transformation', 'limit', 'th', 'first', 'many', 'first', 'moment', 'explicitly', 'moment', 'above', 'nail', 'explicitly', 'incorrectly', 'formula', 'proof', 'limit', 'proof', 'limit', 'equation', 'limit', 'distributed', 'limit', 'feller', 'limit', 'lindeberg-feller', 'limit', 'theorem', 'limit', 'lindeberg-feller', 'limit', 'theorem', 'limit', 'feller', 'limit', 'theorem', 'limit', 'lyapunov', 'limit', 'finite', 'limit', 'theorem', 'limit', 'property', 'limit')
limit	('theorems', 'middle', 'class', 'correspond', 'middle', 'class', 'descriptive', 'class', 'alpha', 'confidence', 'error', 'central', 'theorem', 'frequencies', 'history', 'value', 'point', 'believed', 'believed', 'hypergeometric', 'solution', 'central', 'hypergeometric', 'central', 'theorem', 'central', 'theorem', 'trial', 'binomial', 'essentially', 'number', 'central', 'central', 'central', 'theorem', 'central', 'theorem', 'theorem', 'central', 'theorem', 'theorem', 'central', 'condition', 'central', 'theorem', 'theorem', 'transformation', 'number', 'number', 'inequality', 'central', 'condition', 'central', 'theorem', 'central', 'theorem', 'theorem', 'central', 'theorem', 'central', 'central', 'condition', 'central', 'theorem', 'number', 'number', 'central', 'theorem')
theorems	('limit',)
mantissas	('random',)
random	('mantissas', 'variables', 'demonstrated', 'samples', 'results', 'sample', 'probability', 'participant', 'vector', 'independent', 'set', 'trials', 'midrange', 'sample', 'deviation', 'function', 'variable', 'median', 'sample', 'range', 'sample', 'observation', 'variable', 'wald', 'collection', 'sequence', 'simple', 'method', 'walk', 'process', 'sequence', 'set', 'two', 'two', 'definition', 'motion', 'two-dimensional', 'taken', 'displacement', 'walk', 'walk', 'msd', 'independent', 'independent', 'viewed', 'set', 'algebra', 'probability', 'significance', 'sequence', 'variable', 'case', 'closed', 'process', 'closed', 'scatterings', 'time', 'processes', 'coincidence', 'coincidence', 'variable', 'variable', 'variate', 'set', 'measure', 'variable', 'quantile', 'variable', 'closed', 'baudin', 'closed', 'gun', 'event', 'space', 'variable', 'infinite', 'sequence', 'picked', 'least', 'collection', 'polyomino', 'walk', 'process', 'picked', 'class', 'shuffle', 'cliff', 'number', 'generator', 'number', 'number', 'discrepancy', 'discrepancy', 'shuffle', 'set', 'real', 'law', 'eigenvalue', 'matrix', 'set', 'zero', 'formula', 'number', 'polynomial', 'method', 'number', 'number', 'discrepancy', 'sequence', 'transformation', 'sequence', 'one-dimensional', 'martingale', 'ruin', 'walk', 'variate', 'net', 'mapping', 'noise', 'sphere', 'picking', 'number', 'computer-generated', 'number', 'generated', 'physical', 'number', 'sequence', 'number', 'number', 'sequence', 'number', 'uncorrelated', 'uniform', 'uniform', 'generator', 'sequence', 'number', 'number', 'distribution', 'distribution', 'distribution', 'number', 'matrix', 'consist', 'distribution', 'matrix', 'real', 'matrix', 'density', 'complex', 'set', 'real', 'appearing', 'fibonacci', 'n;', 'matrix', 'matrix', 'matrix', 'fibonacci', 'number', 'number', 'computer-generated', 'uniform', 'transformed', 'string', 'string', 'provide', 'number', 'most', 'number', 'goodness', 'generating', 'distributed', 'number', 'number', 'cliff', 'number', 'sequence', 'variable', 'variable', 'definition', 'variable', 'abbreviation', 'variable', 'variable', 'variable', 'space', 'distribution', 'distribution', 'number', 'number', 'variate', 'variate', 'generated', 'variate', 'distributed', 'p', 'variate', 'variate', 'number', 'number', 'number', 'variable', 'number', 'point', 'seed', 'shuffle', 'discrepancy', 'statistic', 'word', 'mean', 'phenomena', 'based', 'stochastic', 'deterministic', 'deterministic', 'variable', 'family', 'process', 'space', 'variable', 'theory', 'sequence', 'concept', 'set', 'variate', 'quantile', 'variable', 'variable', 'variate', 'order', 'classes', 'symmetric', 'above', 'matrix', 'entries', 'law', 'law', 'matrix', 'sequence', 'fair', 'time', 'walk', 'independent', 'motion', 'distribution', 'variable', 'variable', 'walk', 'walk', 'walk', 'lemma', 'flight', 'walk', 'probability', 'pólya', 'walk', 'constant', 'walk', 'walk', 'calculus', 'walk', 'length', 'walk', 'previous', 'walk', 'physically', 'thermal', 'responsible', 'walk', 'gas', 'walk', 'diffusion', 'walk', 'walk', 'theory', 'walk', 'dimensional', 'walk', 'dimensional', 'walk', 'deal', 'three', 'followed', 'walk', 'symmetric', 'walk', 'step', 'walk', 'dimensional', 'pelya', 'walk', 'constant', 'walk', 'dimensional', 'walk', 'vector', 'unit', 'displacement', 'difference', 'lattice', 'walk', 'infinity', 'walk', 'dimensional', 'pelya', 'walk', 'constant', 'walk', 'dimensional', 'walk', 'lattice', 'walk', 'pelya', 'walk', 'constant', 'walk', 'dimensional', 'pelya', 'walk', 'constant', 'walk', 'dimensional', 'walk', 'walk', 'path', 'walk', 'number', 'constant', 'walk', 'walk', 'process', 'measure', 'motion', 'walk', 'walk', 'step', 'process', 'lemma', 'walk', 'radius', 'sausage', 'statistic', 'variable', 'variable', 'walk', 'walk', 'walk', 'two', 'entries', 'component', 'plot', 'sample', 'test', 'sampling', 'estimator', 'scatter', 'observation', 'variable', 'theory', 'variable', 'variable', 'walk', 'possibly', 'selection', 'selection', 'generation', 'tilted', 'chi-squared', 'doob', 'process', 'memoryless', 'independent', 'independent', 'addition', 'properties', 'sum', 'value', 'variable', 'probability', 'sample', 'variable', 'freedom', 'variable', 'distribution', 'variable', 'distributed', 'variable', 'sequence', 'number', 'size', 'distribution', 'binomial', 'distribution', 'walk', 'distribution', 'walk', 'memoryless', 'one-dimensional', 'tossing', 'walk', 'successful', 'distribution', 'variable', 'set', 'using', 'number', 'generator', 'number', 'two', 'memoryless', 'distribution', 'function', 'variable', 'independent', 'unrelated', 'independent', 'trial', 'process', 'sum', 'theorem', 'independent', 'independent', 'distributed')
variables	('random', 'under', 'number', 'observed', 'namely', 'two', 'examined--in')
multiplication	('number', 'bit', 'two', 'quantities', 'identity', 'ways', 'principle', 'ito', 'table', 'root', 'root')
increases	('density', 'you', 'tends', 'statistically')
density	('increases', 'function', 'probability', 'probability', 'probability', 'probability', 'probability', 'probability', 'probability', 'function', 'probability', 'probability', 'probability', 'function', 'probability', 'probability', 'probability', 'probability', 'probability', 'probability', 'probability', 'function', 'clustering', 'function', 'probability', 'whatsoever', 'error', 'joint', 'function', 'function', 'point', 'probability', 'probability', 'probability', 'probability', 'probability', 'function', 'provided', 'intensity', 'probability', 'occurrence', 'probability', 'parameter', 'probability', 'function', 'stipulated', 'probability', 'probability', 'function', 'probability', 'probability', 'function', 'probability', 'function', 'probability', 'function', 'probability', 'probability', 'probability', 'function', 'edelman', 'random', 'run', 'percolation', 'cumulative', 'function', 'probability', 'probability', 'function', 'spectral', 'probability', 'probability', 'probability', 'probability', 'probability', 'function', 'probability', 'cumulative', 'probability', 'derivative', 'normalized', 'probability', 'probability', 'probability', 'function', 'probability', 'function', 'probability', 'probability', 'probability', 'function', 'probability', 'probability', 'function', 'probability', 'function', 'probability', 'probability', 'probability', 'probability', 'probability', 'average', 'probability', 'probability', 'probability', 'probability', 'function', 'probability', 'probability', 'function', 'mean', 'cars', 'probability', 'probability', 'function', 'probability', 'probability')
rigorously	('hill', 'demonstrated')
demonstrated	('rigorously', 'random', 'pp', 'noting')
samples	('random', 'taken', 'equal', 'taken')
taken	('samples', 'variety', 'samples', 'different', 'average', 'absolute', 'size', 'population', 'sample', 'distribution', 'function', 'point', 'function', 'those', 'mark', 'class', 'moment', 'population', 'step', 'random', 'moment', 'point', 'most', 'function', 'raw', 'those', 'integral', 'over', 'sample', 'population', 'sample', 'population', 'independent', 'standard', 'element', 'standard', 'independent', 'standard', 'element', 'distribution', 'generality', 'uniform', 'entries', 'uniform', 'randomly', 'subject', 'walk', 'along', 'step', 'previous', 'length', 'along', 'step', 'step', 'sign', 'step', 'arbitrary', 'wedges', 'together', 'hypothesis', 'variate', 'two', 'product', 'repeated', 'transform', 'distribution', 'continuous', 'excess', 'standard', 'transform', 'parameter', 'first', 'small', 'iff', 'right')
matthews	('one',)
striking	('one', 'example', 'presented', 'conan')
million	('law', 'real', 'one', 'tosses', 'one')
constants	('real', 'plouffe')
plouffe	('constants', 'symbolic', 'question')
symbolic	('plouffe', 'hypothesis')
database	('begin',)
several	('data', 'disparate', 'computation', 'different', 'test', 'proportions', 'widths', 'common', 'distribution', 'flavors', 'statistical', 'skewness', 'distribution', 'other', 'ambiguities', 'authors', 'sum', 'line', 'one', 'statistic', 'competing', 'though', 'authors', 'net', 'ambiguity', 'possible', 'word', 'different', 'number', 'individual', 'product', 'correction', 'dependent', 'independent', 'test', 'statistical', 'one')
disparate	('several',)
table	('sources', 'below', 'following', 'distribution', 'following', 'summarizes', 'distribution', 'two-way', 'tabular', 'contingency', 'observed', 'contingency', 'contingency', 'two', 'contingency', 'one', 'above', 'extended', 'first', 'adding', 'probability', 'contingency', 'homogeneity', 'contingency', 'statistical', 'contingency', 'following', 'frequency', 'following', 'analytic', 'contingency', 'following', 'summarizes', 'denotes', 'following', 'summarizes', 'following', 'number', 'computation', 'grouped', 'following', 'specified', 'noting', 'following', 'summarizes', 'following', 'summarizes', 'following', 'summarizes', 'following', 'skewness', 'following', 'wilcoxon', 'summarized', 'multiplication', 'two', 'subsequent', 'following', 'first', 'following', 'triangle', 'following', 'small', 'ordered', 'represent', 'observed', 'test', 'larger', 'case', 'freedom', 'following', 'summarizes', 'difference', 'least', 'p', 'following', 'confidence', 'following', 'summarizes', 'following', 'evans', 'approximation', 'p', 'number')
digits	('first', 'compiled')
compiled	('digits', 'benford')
original	('benford', 'denominator', 'paper', 'variance', 'data', 'computed', 'multiple', 'stake', 'plus', 'permutation', 'state', 'fitting', 'tukey', 'tukey', 'formulation', 'none', 'reconstructing')
newspapers	('specific',)
specific	('newspapers', 'probability', 'elements', 'yield', 'et', 'number', 'et', 'plot', 'procedure')
j	('atomic',)
atomic	('j',)
m	('reader', 'estimator', 'arguments', 'estimate', 'estimate', 'constant', 'n;', 'ticks')
reader	('m',)
n	('cost', 'multivariate', 'n;', 'probability', 'first', 'probability', 'problem')
cost	('n',)
o	('x-ray',)
x-ray	('o',)
s	('death', 'defied', 'interquartile', 'set', 'appearing', 'triangular', 'skewness', 'kenney', 'coefficient', 'interquartile', 'number', 'number', 'many', 'many', 'h', 't', 'property', 'entire', 'observed', 'matrices', 'indeed', 'raw', 'case', 'savageau', 'sum', 'zabell')
death	('s',)
average	('probable', 'individual', 'taken', 'proposed', 'deviation', 'deviation', 'statistical', 'deviation', 'absolute', 'absolute', 'measure', 'deviation', 'increase', 'september', 'large', 'number', 'feller', 'moving', 'p', 'actually', 'size', 'two', 'exponentially', 'moving', 'abbreviated', 'moving', 'time', 'moving', 'sequence', 'new', 'plot', 'set', 'wolfram', 'moving', 'time', 'moving', 'mean', 'moving', 'spencer', 'running', 'time', 'moving', 'generate', 'moving', 'moving', 'savitzky', 'using', 'moving', 'time', 'moving', 'spencer', 'moving', 'formula', 'moving', 'smoothing', 'moving', 'periodogram', 'interval', 'jitter', 'volume', 'density', 'probability', 'arbitrary')
probable	('average', 'mean', 'error', 'self', 'most', 'number', 'value', 'error', 'value', 'value', 'error', 'great', 'error', 'error', 'error', 'value', 'function', 'error', 'most', 'value')
error	('following', 'typographical', 'denominator', 'study', 'absolute', 'absolute', 'absolute', 'absolute', 'absolute', 'analysis', 'analysis', 'propagation', 'percentage', 'relative', 'relative', 'accuracy', 'analysis', 'absolute', 'absolute', 'propagation', 'relative', 'roundoff', 'roundoff', 'significant', 'precision', 'analysis', 'interval', 'analysis', 'limit', 'analysis', 'deviation', 'analysis', 'remaining', 'equiripple', 'analysis', 'quantity', 'quantity', 'analysis', 'absolute', 'margin', 'margin', 'percentage', 'percentage', 'relative', 'relative', 'absolute', 'relative', 'denotes', 'division', 'powers', 'propagation', 'propagation', 'analysis', 'absolute', 'accuracy', 'percentage', 'precision', 'relative', 'significant', 'estimate', 'analysis', 'analysis', 'estimator', 'estimator', 'margin', 'estimate', 'margin', 'plus', 'what', 'refers', 'margin', 'normal', 'margin', 'margin', 'analysis', 'interval', 'inverse', 'maximum', 'fixed', 'approximation', 'analysis', 'percentage', 'percentage', 'percentage', 'percentage', 'analysis', 'absolute', 'absolute', 'propagation', 'relative', 'precision', 'analysis', 'absolute', 'accuracy', 'precision', 'propagation', 'relative', 'significance', 'relative', 'absolute', 'relative', 'relative', 'percentage', 'relative', 'relative', 'relative', 'analysis', 'absolute', 'absolute', 'propagation', 'percentage', 'use', 'arithmetic', 'analysis', 'arithmetic', 'propagation', 'digit', 'analysis', 'square', 'estimator', 'estimator', 'estimator', 'estimate', 'standard', 'variance', 'standard', 'standard', 'sample', 'sample', 'standard', 'estimate', 'estimated', 'standard', 'probable', 'sample', 'matrix', 'propagation', 'standard', 'statistical', 'density', 'completely', 'probability', 'small', 'latter', 'sayrafiezadeh', 'correct', 'contained', 'sum', 'case', 'line', 'actual', 'least', 'p', 'term', 'p', 'term', 'normal', 'treatment', 'i', 'type', 'ii', 'wilcoxon', 'population', 'i', 'type', 'ii', 'probable', 'significance', 'i', 'type', 'ii', 'type', 'type', 'false', 'false', 'i', 'type', 'ii', 'wilcoxon', 'statistical', 'i', 'statistical', 'ii', 'statistical', 'ii', 'statistical', 'i', 'se', 'ci', 're', 'distribution', 'cumulant', 'function', 'sign', 'von', 'gauss', 'function', 'erf', 'erf', 'function', 'function', 'normally', 'probable', 'value', 'probable', 'probable', 'probable', 'continuous', 'standard', 'standard', 'standard', 'probable', 'probability')
following	('error', 'table', 'mantissa', 'benford', 'mark', 'table', 'boundaries', 'table', 'value', 'table', 'using', 'equations', 'summarized', 'quartile', 'table', 'function', 'table', 'function', 'table', 'group', 'example', 'table', 'satisfy', 'table', 'separately', 'table', 'distribution', 'table', 'use', 'et', 'table', 'denoted', 'table', 'summarized', 'sequence', 'wolfram', 'start', 'properties', 'finch', 'step', 'step', 'table', 'slade', 'walk', 'p', 'table', 'bloom', 'recurrence', 'summarized', 'table', 'listed', 'entries', 'specificity', 'table', 'consisting', 'markov', 'kind', 'table', 'first', 'table', 'summarized', 'table', 'summarized', 'ball', 'satisfying')
mantissa	('digit', 'following')
a055440	('largest',)
largest	('a055440', 'a055441', 'computer', 'number', 'smallest', 'absolute', 'space', 'set', 'difference', 'smallest')
remainder	('hare', 'droop')
hare	('remainder',)
a055441	('largest',)
droop	('remainder',)
a055442	('benford',)
possessing	('two', 'one', 'three', 'single')
two	('possessing', 'distribution', 'local', 'opposed', 'equal', 'distribution', 'separated', 'least', 'rows', 'rows', 'columns', 'frequency', 'table', 'rows', 'classified', 'test', 'variables', 'value', 'steps', 'contributes', 'possible', 'data', 'point', 'histogram', 'distribution', 'one', 'relationship', 'fewer', 'distinct', 'term', 'completely', 'violet', 'addition', 'multiplication', 'division', 'quantities', 'equal', 'nonsingular', 'gauss', 'correlation', 'covariance', 'random', 'sum', 'random', 'applied', 'elements', 'applied', 'elements', 'follow', 'statisticians', 'low', 'statisticians', 'mean', 'shots', 'summand', 'pieces', 'skewness', 'first', 'appear', 'different', 'variance', 'free', 'involving', 'p', 'independent', 'authors', 'alternative', 'univariate', 'opposed', 'parameter', 'associations', 'no', 'first', 'up', 'probability', 'people', 'least', 'share', 'people', 'birthday', 'chance', 'match', 'intersecting', 'distance', 'distance', 'ruled', 'lie', 'indicated', 'fair', 'tile', 'landing', 'lie', 'game', 'fair', 'tile', 'lie', 'game', 'fair', 'tile', 'lie', 'game', 'fair', 'tile', 'runs', 'identical', 'no', 'consecutive', 'throws', 'even', 'dice', 'probability', 'flip', 'one', 'player', 'least', 'distinct', 'ways', 'least', 'sixes', 'cartridge', 'duelists', 'toss', 'covariance', 'covariance', 'probability', 'people', 'least', 'distinct', 'follow', 'low', 'mean', 'shots', 'shown', 'different', 'uniform', 'other', 'halves', 'interleaving', 'halves', 'length', 'layers', 'table', 'fundamental', 'row', 'no', 'consecutive', 'walk', 'yield', 'self-avoiding', 'concatenating', 'self-avoiding', 'average', 'central', 'midpoint', 'non-parallel', 'degree', 'quantities', 'value', 'axes', 'relationship', 'quantities', 'term', 'other', 'random', 'covariance', 'combination', 'append', 'added', 'fourth', 'containing', 'distinguishable', 'permutation', 'type', 'type', 'set', 'different', 'determination', 'test', 'performing', 'mean', 'mean', 'test', 'results', 'dot', 'plot', 'data', 'plot', 'data', 'data', 'mean', 'universes', 'mean', 'normal', 'association', 'categorical', 'exist', 'vector', 'paired', 'level', 'taken', 'observation', 'main', 'distribution', 'free', 'one', 'notational', 'testing', 'observed', 'dispersion', 'ratio', 'independent', 'distribution', 'free', 'distance', 'difference', 'independent', 'distribution', 'independently', 'difference', 'normally', 'mean', 'normal', 'variate', 'independent', 'approximation', 'decimal', 'difference', 'product', 'normally', 'sum', 'normally', 'testing', 'observed', 'difference', 'observed', 'difference', 'uniform', 'distribution', 'possible', 'moment', 'distribution', 'probability', 'dependent', 'function', 'satisfies', 'random', 'memoryless', 'other', 'memoryless', 'conjectured', 'parameter', 'possible')
term	('mode', 'bimodal', 'frequency', 'two', 'mode', 'unimodal', 'last', 'minimax', 'power', 'sample', 'gupta', 'introduced', 'power', 'dressel', 'introduced', 'power', 'population', 'raw', 'raw', 'multivariate', 'function', 'characteristic', 'central', 'raw', 'multivariate', 'wherever', 'derivative', 'appearing', 'above', 'satisfies', 'function', 'central', 'transformations', 'multivariate', 'use', 'root-mean-square', 'use', 'second', 'third', 'sample', 'containing', 'first', 'second', 'second', 'third', 'plugging', 'use', 'second', 'expanding', 'braces', 'sine', 'usage', 'hawkes', 'use', 'assigned', 'exist', 'adjective', 'oeis', 'domain', 'mathematics', 'domain', 'unfortunately', 'even', 'worth', 'unfortunate', 'initial', 'derived', 'p', 'first', 'net', 'net', 'archaic', 'computer-generated', 'number', 'reserved', 'form', 'refers', 'ordinary', 'explicitly', 'first', 'pair', 'wiener', 'intended', 'using', 'quantity', 'two', 'quantities', 'regression', 'regression', 'form', 'length', 'goulden', 'order', 'binomial', 'error', 'satisfies', 'error', 'satisfies', 'obtain', 'expansion', 'likelihood', 'likelihood', 'negative', 'use', 'practice', 'null', 'null', 'null', 'null', 'size', 'signal', 'work', 'distribution', 'use', 'finite', 'gaussian', 'finite', 'meijer', 'distribution', 'heaviside', 'oeis', 'expansion', 'continuous', 'order', 'higher', 'lerch', 'double', 'reserves', 'distinct', 'series', 'rate', 'unfortunately', 'mean', 'individual', 'sum')
bimodal	('term', 'definition', 'descriptive', 'statistics', 'distribution', 'peaks', 'distribution', 'statistics', 'unimodal', 'one', 'statistic', 'mode', 'statistic', 'mode', 'statistic', 'mode', 'distribution', 'distribution')
refers	('distribution', 'distribution', 'mathematics', 'group', 'distribution', 'distribution', 'error', 'confidence', 'excess', 'quantity', 'probability', 'occurrence', 'likelihood', 'past', 'mathematics', 'plane', 'term', 'fact', 'hypothesis', 'statement')
local	('two', 'maxima', 'statistic', 'maximum', 'maximum', 'mark', 'maximum', 'maximum', 'single', 'maximum', 'loess', 'regression', 'loess', 'regression', 'regression', 'discrepancy', 'discrepancy', 'discrepancy', 'discrepancy', 'discrepancy', 'cube', 'discrepancy', 'discrepancy', 'discrepancy', 'discrepancy', 'discrepancy', 'discrepancy')
maxima	('local', 'opposed', 'high-water', 'running', 'sequence', 'running', 'unique')
opposed	('maxima', 'two', 'variable', 'many', 'variable', 'one', 'variable', 'two', 'toss', 'based', 'strenuously', 'principle', 'step')
equal	('two', 'most', 'proportions', 'samples', 'theoretical', 'low', 'size', 'shown', 'zero', 'distribution', 'less', 'less', 'quantities', 'smallest', 'sum', 'expectation', 'conditional', 'two', 'distribution', 'kurtosis', 'proper', 'mean', 'distribution', 'third', 'power', 'expand', 'zero', 'variance', 'second', 'variance', 'second', 'stake', 'number', 'probability', 'shown', 'quadrilateral', 't', 'proven', 'bankrupt', 'ratio', 'even', 'greater', 'observed', 'p-value', 'observed', 'alternative', 'keynes', 'expectation', 'feller', 'point', 'number', 'distributed', 'densities', 'second', 'step', 'length', 'value', 'number', 'number', 'number', 'variate', 'comparison', 'alpha', 'comparison', 'represent', 'greater', 'less', 'because', 'greater', 'observed', 'quite', 'spaced', 'mean', 'setting', 'various', 'case', 'double', 'right', 'sample', 'selection', 'selection', 'likelihood', 'ratio', 'less', 'number', 'population')
most	('equal', 'common', 'coefficient', 'easily', 'observations', 'occurring', 'mean', 'efficient', 'th', 'common', 'computer', 'mid-2002', 'common', 'bits', 'prevalent', 'precision', 'p', 'authors', 'determined', 'recent', 'kurtosis', 'encountered', 'moment', 'taken', 'moment', 'common', 'himself', 'progress', 'surprisingly', 'common', 'distribution', 'typically', 'domain', 'set', 'out', 'pennies', 'case', 'a143163', 'letter', 'set', 'stationary', 'utilized', 'position', 'frequent', 'shuffled', 'likely', 'language', 'random', 'letter', 'set', 'surprisingly', 'probable', 'size', 'common', 'estimate', 'what', 'simplest', 'applied', 'uncertainties', 'general', 'estimate', 'what', 'fit', 'common', 'pseudoinverse', 'encountered', 'criterion', 'common', 'operator', 'important', 'simplest', 'conservative', 'test', 'applied', 'statistic', 'order', 'distribution', 'normal', 'simplest', 'parameter', 'common', 'distribution', 'common', 'distribution', 'common', 'parameter', 'common', 'distribution', 'probable', 'statistic', 'nolan', 'convenient')
slight	('value', 'corruption', 'maximum', 'corruption', 'despite', 'accompanied', 'paucity')
corruption	('slight', 'slight')
definition	('bimodal', 'measurement', 'record', 'basis', 'pearson', 'convenient', 'outlier', 'quantile', 'violate', 'independent', 'nonnegative', 'basis', 'pearson', 'unimodal', 'basis', 'pearson', 'prefer', 'sample', 'characteristic', 'symmetric', 'random', 'intuitive', 'deviation', 'induction', 'sample', 'through', 'standard', 'p', 'no', 'using', 'multivariate', 'imprecise', 'because', 'occur', 'similar', 'similar', 'spp', 'above', 'modified', 'different', 'stationary', 'alternative', 'intensity', 'different', 'random', 'above', 'extended', 'differential', 'ito', 'angle', 'guarantees', 'property', 'quantities', 'closely-related', 'usual', 'calls', 'series', 'constant', 'solving', 'binomial', 'type', 'memoryless', 'case', 'geometric', 'memoryless', 'close')
multimodal	('mode', 'trimodal', 'mode', 'trimodal', 'descriptive', 'mode', 'unimodal', 'mode', 'trimodal')
trimodal	('multimodal', 'unimodal', 'multimodal', 'mode', 'unimodal', 'mode', 'descriptive', 'multimodal', 'unimodal')
unimodal	('trimodal', 'bimodal', 'distribution', 'distribution', 'hold', 'one', 'trimodal', 'hold', 'multimodal', 'term', 'definition', 'descriptive', 'trimodal', 'distribution', 'distribution', 'sequence', 'hold', 'noncentral', 'univariate', 'single', 'distribution', 'distribution')
separated	('two', 'slightly', 'disk')
peaks	('bimodal',)
interval	('data', 'boundaries', 'boundaries', 'class', 'class', 'class', 'class', 'class', 'class', 'class', 'middle', 'class', 'class', 'descriptive', 'class', 'class', 'class', 'class', 'denoted', 'frequency', 'class', 'cumulative', 'class', 'lie', 'over', 'integrates', 'over', 'you', 'confidence', 'confidence', 'measurement', 'confidence', 'interest', 'confidence', 'symmetric', 'function', 'normal', 'within', 'confidence', 'centered', 'confidence', 'representative', 'confidence', 'error', 'confidence', 'confidence', 'standard', 'confidence', 'error', 'completely', 'class', 'remaining', 'variation', 'sequence', 'variation', 'moment', 'over', 'root-mean-square', 'root-mean-square', 'th', 'corrected', 'class', 'histogram', 'ci', 'first', 'solve', 'confidence', 'mean', 'mean', 'data', 'bartoš', 'process', 'stationary', 'pointed', 'notion', 'stationary', 'difference', 'stationarity', 'notion', 'stationarity;', 'vere-jones', 'stationary', 'within', 'probability', 'domain', 'whereas', 'probability', 'point', 'notion', 'half-open', 'volume', 'st', 'halving', 'subsequent', 'divide', 'number', 'lie', 'real', 'class', 'frequency', 'plotting', 'sample', 'class', 'dot', 'confidence', 'hypothesis', 'significance', 'confidence', 'p', 'time', 'uniformly', 'average', 'ci', 'over', 'special', 'unit', 'probability', 'value', 'half-infinite', 'within', 'probability', 'small', 'confidence', 'erf', 'erfc', 'over', 'wolfram', 'goulden', 'multivariate', 'variate', 'delta', 'distribution', 'written', 'variate', 'delta', 'variate', 'delta', 'variate', 'delta', 'independent', 'probability', 'small', 'probability', 'small', 'essentially', 'one-dimensional')
point	('data', 'outside', 'drawing', 'preferable', 'curve', 'h', 'two', 'either', 'find', 'curve', 'lorenz', 'correspondingly', 'lorenz', 'example', 'far', 'outlier', 'greatly', 'divide', 'divide', 'relative', 'frequency', 'initial', 'initial', 'vector', 'decimal', 'decimal', 'precision', 'fisher', 'population', 'estimator', 'estimator', 'estimation', 'taken', 'absolute', 'taken', 'statistical', 'number', 'multivariate', 'temporal', 'time', 'temporal', 'processes', 'temporal', 'process', 'simple', 'simple', 'process', 'univariate', 'function', 'process', 'exciting', 'process', 'temporal', 'process', 'density', 'estimated', 'orientation', 'wichura', 'estimator', 'parameter', 'estimator', 'temporal', 'limit', 'process', 'temporal', 'process', 'analysis', 'process', 'theory', 'intensity', 'process', 'talk', 'processes', 'function', 'process', 'measure', 'process', 'measure', 'falling', 'function', 'process', 'stationary', 'process', 'stationary', 'stationary', 'process', 'analysis', 'process', 'stationary', 'process', 'marked', 'process', 'marked', 'marked', 'process', 'process', 'process', 'marked', 'process', 'simple', 'marking', 'marked', 'process', 'space', 'process', 'correcting', 'process', 'exciting', 'process', 'simple', 'process', 'spatial', 'process', 'temporal', 'process', 'temporal', 'process', 'multidimensional', 'process', 'multidimensional', 'process', 'marked', 'multidimensional', 'processes', 'multidimensional', 'process', 'marked', 'process', 'process', 'process', 'p-value', 'probability', 'probability', 'process', 'oftentimes', 'processes', 'realization', 'example', 'processes', 'vere-jones', 'processes', 'scatter', 'process', 'marked', 'process', 'correcting', 'process', 'exciting', 'process', 'simple', 'process', 'spatial', 'process', 'temporal', 'process', 'temporal', 'process', 'multidimensional', 'multidimensional', 'process', 'process', 'process', 'inhibits', 'self', 'correcting', 'process', 'marked', 'process', 'process', 'process', 'exciting', 'process', 'simple', 'process', 'spatial', 'process', 'temporal', 'process', 'temporal', 'process', 'occurrence', 'exciting', 'process', 'marked', 'process', 'process', 'process', 'correcting', 'process', 'simple', 'process', 'spatial', 'process', 'temporal', 'process', 'temporal', 'process', 'simple', 'process', 'time', 'th', 'simple', 'process', 'marked', 'process', 'process', 'process', 'correcting', 'process', 'exciting', 'process', 'spatial', 'process', 'temporal', 'process', 'temporal', 'process', 'spatial', 'process', 'process', 'spatial', 'process', 'marked', 'process', 'process', 'process', 'correcting', 'process', 'exciting', 'process', 'simple', 'process', 'temporal', 'process', 'temporal', 'process', 'spatial-temporal', 'process', 'process', 'spatial-temporal', 'process', 'collection', 'spatial-temporal', 'processes', 'spatiotemporal', 'spatio-temporal', 'space-time', 'temporal', 'process', 'marked', 'process', 'process', 'process', 'correcting', 'process', 'exciting', 'process', 'simple', 'process', 'spatial', 'process', 'temporal', 'process', 'notion', 'intuitively', 'process', 'lying', 'interval', 'process', 'stationary', 'processes', 'stationary', 'process', 'conclude', 'process', 'stationary', 'process', 'probabilities', 'probabilities', 'value', 'probability', 'temporal', 'process', 'temporal', 'processes', 'liam', 'temporal', 'processes', 'temporal', 'processes', 'temporal', 'process', 'temporal', 'processes', 'temporal', 'process', 'marked', 'process', 'process', 'process', 'correcting', 'process', 'exciting', 'process', 'simple', 'process', 'spatial', 'process', 'temporal', 'process', 'deviation', 'set', 'discrepancy', 'hammersley', 'set', 'hammersley', 'set', 'set', 'set', 'hammersley', 'set', 'inflection', 'applying', 'shown', 'set', 'half-open', 'hammersley', 'hammersley', 'hammersley', 'set', 'spherical', 'along', 'ball', 'picking', 'sphere', 'picking', 'low-discrepancy', 'generating', 'equal', 'st', 'still', 'generated', 'next', 'previous', 'sequence', 'stopping', 'convergence', 'quasirandom', 'hammersley', 'set', 'sphere', 'starting', 'random', 'starting', 'seen', 'view', 'theory', 'distributed', 'halton', 'set', 'hammersley', 'set', 'maximally', 'highly', 'next', 'previous', 'reaching', 'including', 'number', 'reaching', 'including', 'number', 'starting', 'again', 'one', 'never', 'lattice', 'paths', 'maximum', 'lattice', 'twice', 'intersect', 'triangle', 'respective', 'lie', 'minimizing', 'disproportionate', 'along', 'difference', 'weighted', 'function', 'deviation', 'disproportionately', 'vertical', 'fitted', 'fitted', 'estimator', 'along', 'using', 'perpendicular', 'line', 'function', 'fitting', 'using', 'cartesian', 'range', 'drew', 'joined', 'falling', 'formed', 'lie', 'plotting', 'finding', 'cuzzi', 'best', 'moving', 'spencer', 'moving', 'smoothing', 'spencer', 'moving', 'fixed', 'oeis', 'uppermost', 'nail', 'distribution', 'process')
bin	('fall', 'descriptive', 'statistics', 'packing', 'statistics', 'class', 'moment', 'class', 'draw', 'falling', 'draw', 'above', 'labeling', 'spaced', 'members', 'members', 'class', 'distribution', 'number', 'range', 'number', 'bihistogram', 'class', 'single')
packing	('bin', 'problem')
problem	('packing', 'histogram', 'haberdasher', 'hinge', 'case', 'example', 'binary', 'two-dimensional', 'moment', 'moment', 'moment', 'moment', 'moment', 'moment', 'moment', 'moment', 'asks', 'birthday', 'probability', 'world', 'sultan', 'dowry', 'needle', 'asks', 'solomon', 'first', 'needle', 'probability', 'needle', 'clean', 'tile', 'needle', 'asks', 'apart', 'first', 'trial', 'extended', 'buffon', 'needle', 'probability', 'needle', 'clean', 'tile', 'square', 'infinite', 'tile', 'probability', 'needle', 'buffon', 'needle', 'little', 'presented', 'birthday', 'law', 'collector', 'probability', 'birthday', 'solved', 'de', 'mere', 'probability', 'pepys', 'pepys', 'probability', 'mere', 'world', 'asks', 'world', 'probability', 'birthday', 'small', 'needle', 'buffon', 'needle', 'chernoff', 'mere', 'dice', 'sharing', 'statistical', 'quasi-monte', 'desirable', 'solution', 'finding', 'minimized', 'solved', 'solution', 'inverse', 'equation', 'behrens', 'statistical', 'indicate', 'forecasting', 'determination', 'behrens', 'galton', 'behrens', 'gaussian', 'value', 'savageau', 'n', 'finding', 'picking', 'asks')
histogram	('problem', 'above', 'mark', 'sheppard', 'set', 'boundaries', 'relative', 'grouped', 'distribution', 'ogive', 'unique', 'two', 'plot', 'least', 'interval', 'plot', 'pareto', 'method', 'hinge', 'interquartile', 'chart', 'plot', 'stem', 'computed', 'function', 'above', 'number', 'wolfram', 'data', 'statistical', 'polygon', 'sector', 'plot')
skewness	('quartile', 'quartile', 'bowley', 'descriptive', 'mode', 'pearson', 'pearson', 'coefficients', 'coefficients', 'mode', 'mode', 'statistical', 'statistical', 'mode', 'head', 'statistical', 'population', 'sample', 'moment', 'statistic', 'sample', 'moment', 'correction', 'unbiased', 'kurtosis', 'mean', 'standard', 'mode', 'power', 'sequence', 'standard', 'momental', 'momental', 'moment', 'mode', 'function', 'mode', 'bowley', 'mean', 'pearson', 'coefficient', 'first', 'incorrectly', 'pearson', 'bowley', 'pearson', 'mode', 'mode', 'kurtosis', 'measure', 'reverse', 'two', 'several', 'type', 'notation', 'confusing', 'distribution', 'confusingly', 'wolfram', 'estimator', 's', 'table', 'number', 'bernoulli', 'form', 'momental', 'pearson', 'pearson', 'pearson', 'quartile', 'quartile', 'momental', 'bowley', 'gamma', 'graph', 'kurtosis', 'momental', 'standard', 'moment', 'kurtosis', 'kurtosis', 'kurtosis', 'kurtosis', 'kurtosis', 'kurtosis', 'kurtosis', 'kurtosis', 'kurtosis', 'kurtosis', 'kurtosis', 'kurtosis', 'kurtosis', 'kurtosis', 'kurtosis', 'kurtosis', 'kurtosis', 'kurtosis', 'kurtosis', 'kurtosis', 'kurtosis', 'kurtosis', 'kurtosis', 'kurtosis', 'kurtosis', 'kurtosis', 'kurtosis', 'kurtosis', 'kurtosis', 'kurtosis', 'kurtosis', 'kurtosis', 'kurtosis', 'kurtosis', 'kurtosis', 'kurtosis', 'kurtosis', 'kurtosis', 'kurtosis', 'kurtosis', 'kurtosis', 'kurtosis', 'kurtosis', 'heavy', 'parameter')
quartile	('skewness', 'skewness', 'difference', 'statistic', 'statistical', 'hinge', 'statistical', 'below', 'outliers', 'quantile', 'plot', 'variate', 'plot', 'variate', 'rank', 'including', 'first', 'denoted', 'similarly', 'following', 'sample', 'perles', 'descriptive', 'quantile', 'deviation', 'deviation', 'variation', 'range', 'deviation', 'range', 'range', 'variation', 'range', 'variation', 'range', 'range', 'deviation', 'deviation', 'deviation', 'skewness', 'skewness', 'median', 'draw', 'range', 'statistical', 'standard')
coefficient	('defied', 'gini', 'gini', 'gini', 'most', 'gini', 'above', 'gini', 'gini', 'descriptive', 'asymmetry', 'lorenz', 'asymmetry', 'summary', 'asymmetry', 'asymmetry', 'descriptive', 'gini', 'lorenz', 'gini', 'lorenz', 'gini', 'lorenz', 'asymmetry', 'variation', 'variation', 'variation', 'descriptive', 'correlation', 'covariance', 'graph', 'dividing', 'interpret', 'skewness', 'pearson', 'second', 'bowley', 's', 'variation', 'variation', 'variation', 'derive', 'correlation', 'bivariate', 'probability', 'divide', 'spearman', 'correlation', 'undesirable', 'correlation', 'difference', 'computed', 'correlation', 'easier', 'correlation', 'rank', 'correlation', 'least', 'hypergeometric', 'independent', 'independent', 'probability', 'triangle', 'correlation', 'statistical', 'correlation', 'wilcoxon', 'correlating', 'correlation', 'cross', 'cross-correlation', 'pearson', 'correlation', 'correlation', 'first', 'correlation', 'correlation', 'denoted', 'correlation', 'product-moment', 'product-moment', 'correlation', 'linear', 'correlation', 'important', 'correlation', 'other', 'correlation', 'independent', 'correlation', 'regression', 'correlation', 'bivariate', 'regression', 'spearman', 'correlation', 'variance', 'population', 'hypergeometric', 'distribution', 'observed', 'sample', 'correlation', 'bivariate', 'correlation', 'fisher', 'correlation', 'spherical', 'correlation', 'regression', 'correlation', 'regression', 'regression', 'proportion', 'correlation', 'interpolation', 'regression', 'residual', 'least', 'least', 'regression', 'self', 'regression', 'regression', 'regression', 'correlation', 'least', 'residual', 'generating', 'johnson', 'bloom', 'data', 'correlation', 'difference', 'correlation', 'covariance', 'identical', 'correlation', 'discrete', 'correlation', 'continuous', 'correlation', 'floor', 'distribution', 'above', 'characterized', 'distribution', 'multinomial', 'multinomial', 'distribution', 'defining', 'correlation')
defied	('coefficient', 's')
interquartile	('s', 'statistics', 'range', 'same', 'hinge', 'range', 'third', 'range', 'range', 'range', 'times', 'hinge', 'range', 'third', 'statistic', 'range', 'third', 'statistic', 'range', 's', 'time', 'time', 'histogram', 'range')
wolfram	('range', 'data', 'distribution', 'p', 'language', 'respectively', 'form', 'number', 'version', 'version', 'version', 'distribution', 'skewness', 'sigma', 'x2', 'sigma', 'undocumented', 'following', 'integer', 'size', 'matrix', 'encoding', 'charts', 'plot', 'using', 'plot', 'histogram', 'data', 'chart', 'data', 'data', 'data', 'average', 'distribution', 'distribution', 'distribution', 'distribution', 'function', 'parameter', 'function', 'function', 'parameter', 'function', 'p', 'distribution', 'function', 'distribution', 'function', 'distribution', 'constant', 'function', 'polynomial', 'distribution', 'distribution', 'interval', 'parameter', 'freedom', 'multivariatetdistribution', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'above', 'distribution', 'distribution', 'distribution', 'distribution')
bowley	('data', 'skewness', 'moment', 'skewness', 'moment', 'skewness', 'coefficient', 'moment', 'skewness', 'index', 'index', 'formula', 'indices', 'index')
pearson	('range', 'mode', 'skewness', 'skewness', 'definition', 'mode', 'statistic', 'mode', 'definition', 'mode', 'statistic', 'mode', 'definition', 'mode', 'denoted', 'notation;', 'deviation', 'mode', 'deviation', 'mode', 'property', 'iii', 'kenney', 'mode', 'mode', 'skewness', 'deviation', 'first', 'coefficient', 'mode', 'statistics`descriptivestatistics`', 'second', 'data', 'skewness', 'skewness', 'mode', 'distribution', 'type', 'skewness', 'mode', 'skewness', 'skewness', 'romanovsky', 'kenney', 'make', 'correlation', 'coefficient', 'correlation', 'pcc', 'perason', 'correlation', 'correlation', 'karl', 'limiting', 'either', 'chi-square', 'practice', 'statistic', 'neyman', 'lemma', 'distribution', 'type', 'using', 'function', 'system', 'discussed', 'see', 'kenney', 'curve', 'written', 'system', 'excess', 'type', 'distribution', 'type')
coefficients	('skewness', 'skewness')
ratio	('measure', 'summary', 'gini', 'area', 'absolute', 'measured', 'variance', 'tile', 'shaded', 'equal', 'pennies', 'mortality', 'probability', 'mills', 'probability', 'likelihood', 'maximum', 'likelihood', 'probability', 'likelihood', 'maximum', 'mills', 'hazard', 'mills', 'probability', 'fraction', 'function', 'distribution', 'distribution', 'function', 'graham', 'correlation', 'covariance', 'correlation', 'population', 'confluent', 'correlation', 'regression', 'likelihood', 'likelihood', 'statistical', 'likelihood', 'sensitivity', 'likelihood', 'likelihood', 'statistical', 'likelihood', 'sensitivity', 'likelihood', 'log', 'likelihood', 'paired', 'lexis', 'lexis', 'set', 'lexis', 'subnormal', 'satisfies', 'distribution', 'distribution', 'statistic', 'two', 'f', 'continuous', 'variate', 'variate', 'gamma', 'distribution', 'distribution', 'jacobian', 'distribution', 'gaussian', 'distribution', 'normal', 'distribution', 'normal', 'distribution', 'normal', 'normal', 'distribution', 'system', 'distribution', 'normal', 'distribution', 'independent', 'distribution', 'distribution', 'normal', 'distribution', 'normal', 'distribution', 'uniform', 'distribution', 'uniform', 'distribution', 'uniform', 'distribution', 'uniform', 'uniform', 'distribution', 'distribution', 'distribution', 'uniform', 'distribution', 'equal', 'probabilities', 'galaxies', 'gravitational', 'function', 'distribution', 'distribution', 'distribution', 'uniform', 'distribution', 'distribution', 'uniform', 'distribution')
size	('measure', 'measure', 'clarity', 'classes', 'computing', 'unordered', 'data', 'mean', 'dixon', 'increasing', 'one', 'equal', 'statistical', 'ordered', 'data', 'individual', 'less', 'lorenz', 'sample', 'individual', 'individual', 'lorenz', 'lorenz', 'midrange', 'percentile', 'same', 'similar', 'sample', 'tends', 'word', 'word', 'margin', 'first', 'taken', 'population', 'unbiased', 'sample', 'sample', 'sample', 'estimate', 'sample', 'sample', 'expectation', 'mean', 'sample', 'sample', 'self-excited', 'take', 'calculate', 'obtain', 'population', 'allowed', 'because', 'sample', 'sample', 'pp', 'parameter', 'needle', 'parameter', 'namely', 'depend', 'type', 'entries', 'step', 'most', 'average', 'wolfram', 'summarized', 'nose', 'eye', 'eyebrow', 'mouth', 'mouth', 'karl', 'region', 'region', 'neyman', 'sample', 'sample', 'sample', 'sample', 'number', 'sample', 'term', 'sample', 'sampling', 'distribution', 'silver', 'suppose', 'board', 'random', 'fixed', 'become', 'completely')
clarity	('size', 'descriptive')
word	('many', 'population', 'quantile', 'extreme', 'common', 'roughly', 'harmonic', 'frequency', 'inversely', 'zipf', 'limited', 'size', 'processor', 'size', 'one', 'plus', 'higher', 'markov', 'usage', 'mean', 'net', 'qualification', 'random', 'greek', 'counterpart', 'several', 'proportion', 'written', 'mutually', 'mathematicians')
specialized	('many',)
mathematics	('meaning', 'refers', 'pure', 'term', 'pure', 'branch', 'studies', 'refers', 'meaning', 'mathematical', 'either', 'topics', 'biology', 'journals')
group	('refers', 'objects', 'class', 'factorization', 'high', 'consisting', 'denoting', 'existing', 'objects', 'under', 'stochastic', 'following', 'stochastic', 'clusters', 'out', 'matching', 'out', 'same', 'out', 'data', 'stochastic', 'stochastic', 'weighted', 'symmetric', 'isolated', 'adjacent', 'isolated', 'consecutive', 'change', 'analysis', 'th', 'anova', 'balanced', 'compared')
objects	('group', 'common', 'group', 'possibly', 'picked', 'time', 'been')
property	('common', 'characteristic', 'through', 'function', 'mean', 'pearson', 'type', 'satisfies', 'addition', 'slovin', 's', 'expected', 'number', 'fit', 'desirable', 'definition', 'memoryless', 'equipartition', 'central')
characteristic	('property', 'statistics', 'class', 'class', 'set', 'function', 'elsewhere', 'example', 'function', 'definition', 'function', 'term', 'function', 'moment', 'function', 'series', 'function', 'p', 'function', 'cumulant', 'function', 'moment', 'function', 'moment', 'deviation', 'moment', 'function', 'moment', 'function', 'series', 'qed', 'form', 'population', 'vacuum', 'matrix', 'series', 'function', 'approximated', 'part', 'expansion', 'normalized', 'gamma', 'seen', 'via', 'mean', 'excess', 'function', 'excess', 'theta', 'using', 'excess', 'distribution', 'noting', 'distribution', 'excess', 'excess', 'student', 'excess', 'distribution', 'function', 'use', 'success', 'function', 'case', 'defining', 'excess', 'stability')
conjugacy	('class', 'number', 'class')
grouping	('class', 'data')
binned	('data', 'computation', 'ends', 'order')
computation	('binned', 'frequency', 'easier', 'several', 'simple', 'precision', "precision'", 'always', 'concepts', 'done', 'carry', 'variance', 'sample', 'table', 'been', 'pass', 'variance', 'central', 'variance', 'standard', 'variance', 'sample', 'done', 'general', 'discrepancy', 'huge', 'stopping', 'seed', 'whereas')
kenney	('distribution', 'boundaries', 'value', 'asymmetry', 'frequency', 'quantity', 'estimate', 'large', 'asymmetry', 'deviation', 'mode', 'statistical', 'value', 'authors', 'use', 'moment', 'pp', 'estimator', 'special', 'estimator', 'kendall', 'sample', 'asymmetry', 'estimator', 'noted', 'sample', 'p', 'p', 'excess', 'normal', 'kaplansky', 'moment', 'p', 'pearson', 'variance', '◇', 'plugging', 'notation', 'p', 'encountered', 'p', 's', 'function', 'mean', 'pearson', 'estimator', 'quantity', 'correlation', 'probabilities', 'variance', 'case', 'function', 'normal', 'slope', 'line', 'appear', 'line', 'function', 'inverse', 'rewritten', 'p', 'pp', 'value', 'uspensky', 'p', 'distribution', 'curve', 'distribution', 'includes', 'distribution', 'transforming', 'craig', 'pearson', ';', ';', 'population')
p	('range', 'class', 'denoted', 'midrange', 'basis', 'denoted', 'efficiency', 'median', 'basis', 'small', 'statement', 'wolfram', 'distribution', 'value', 'first', 'rose', 'most', 'carver', 'maximum', 'analogy', 'basis', 'markov', 'correction', 'bessel', 'first', 'morrison', 'characteristic', 'maclaurin', 'kenney', 'kenney', 'denoted', 'kurtosis', 'observation', 'westfall', 'kenney', 'first', 'rose', 'algebra', 'kenney', 'due', 'kenney', 'abramowitz', 'abramowitz', 'confusingly', 'normal', 'function', 'raw', 'standard', 'definition', 'zwillinger', 'standard', 'two', 'standardized', 'trivariate', 'denoted', 'ad', 'solomon', 'buffon', 'above', 'solomon', 'further', 'first', 'coin', 'coincidence', 'evans', 'hazard', 'likelihood', 'mills', 'strictly', 'value', 'use', 'average', 'value', 'probability', 'value', 'term', 'net', 'slightly', 'random', 'indicate', 'stochastic', 'absolutely', 'borel-tanner', 'borel', 'konig', 'variance', 'correlation', 'merit', 'following', 'error', 'kenney', 'slightly', 'error', 'kenney', 'box-and-whisker', 'variation', 'tukey', 'testing', 'value', 'hypothesis', 'value', 'manova', 'interval', 'value', 'event', 'mathematical', 'denoted', 'beta', 'above', 'central', 'evans', 'table', 'distribution', 'analog', 'order', 'wolfram', 'had', 'distribution', 'normal', 'among', 'normal', 'use', 'function', 'gamma', 'first', 'inverse', 'snedecor', 'inverse', 'confidence', 'moment-generating', 'table', 'zwillinger', 'mean', 'defining', 'raw', 'distribution', 'evans', 'calling', 'even', 'survival', 'equation', 'lindeberg', 'lindeberg')
boundaries	('interval', 'interval', 'class', 'class', 'class', 'kenney', 'class', 'descriptive', 'class', 'class', 'class', 'class', 'following', 'class', 'histogram', 'total')
middle	('limit', 'class', 'limit', 'interval', 'because', 'slots', 'upper')
mark	('following', 'absolute', 'class', 'class', 'class', 'class', 'histogram', 'class', 'midvalue', 'class', 'descriptive', 'absolute', 'occur', 'measurements', 'water', 'descriptive', 'water', 'high', 'above', 'water', 'local', 'computed', 'class', 'taken', 'immigrants', 'irrelevant', 'time', 'space', 'space', 'space', 'space', 'process', 'space', 'irrelevant', 'irrelevant', 'event', 'th', 'irrelevant', 'analysis', 'space')
summarizes	('table', 'classes', 'table', 'number', 'table', 'probabilities', 'table', 'table', 'mean', 'table', 'mean', 'accurately', 'connection', 'quickly', 'data', 'table', 'names', 'table', 'expected')
classes	('summarizes', 'size', 'algorithm', 'special', 'random', 'various', 'distribution', 't', 'ix-xii')
set	('class', 'class', 'class', 'data', 'histogram', 'drawing', 'straight', 'records', 'random', 'statistic', 'data', 'divide', 'data', 'mode', 'observations', 'data', 'left', 'data', 'right', 'mode', 'data', 'mode', 'ordered', 'actual', 'throws', 'data', 'specified', 'based', 'down', 'arithmetic', 'mean', 'fact', 'nonsingular', 'quantities', 'characteristic', 'function', 'simple', 'random', 'statistical', 'statistical', 'time', 's', 'finally', 'mean', 'mean', 'mean', 'deviation', 'data', 'data', 'msd', 'displacements', 'quantities', 'storing', 'sample', 'running', 'variance', 'distribution', 'data', 'deviation', 'cluster-based', 'elements', 'rate', 'random', 'subject', 'sample', 'conditional', 'inclusion', 'a114602', 'sample', 'perpendicular', 'most', 'real', 'meaning', 'connected', 'integral', 'denotes', 'expected', 'sense', 'unity', 'kolmogorov', 'general', 'space', 'order', 'multidimensional', 'baudin', 'closed', 'probabilities', 'dice', 'event', 'variate', 'random', 'most', 'complement', 'written', 'conditional', 'function', 'transformed', 'closed', 'closed', 'time', 'space', 'event', 'possible', 'formally', 'possible', 'largest', 'tail', 'possible', 'locations', 'locations', 'assumed', 'assumed', 'two-element', 'further', 'index', 'finite', 'discrete', 'time', 'point', 'uniform', 'computationally', 'unit', 'eigenvalues', 'random', 'point', 'order', 'point', 'order', 'leading', 'point', 'point', 'generalized', 'above', 'point', 'random', 'unit', 'point', 'satisfying', 'net', 'even', 'net', 'mapping', 'net', 'directed', 'fiber', 'point', 'net', 'point', 'pseudorandom', 'complex', 'random', 'large', 'space', 'unit', 'index', 'probability', 'point', 'hammersley', 'point', 'monte', 'experiment', 'random', 'most', 'subject', 'restrictions', 'addition', 'value', 'data', 'curve', 'through', 'deviation', 'data', 'line', 'overdetermined', 'overdetermined', 'again', 'up', 'through', 'residual', 'residual', 'plot', 'data', 'two', 'plot', 'value', 'quantities', 'quantities', 'adjacent', 'come', 'data', 'above', 'identical', 'identical', 'comparison', 'alpha', 'possibilities', 'hypothesis', 'possibilities', 'measured', 'comparison', 'average', 'data', 'modification', 'data', 'element', 'probability', 'variance', 'lexis', 'out', 'identical', 'certain', 'ratio', 'variance', 'lexis', 'mean', 'find', 'expression', 'distribution', 'restricting', 'restricting', 'positive', 'random', 'under', 'calling', 'variate')
factorization	('group', 'method')
method	('factorization', 'class', 'computing', 'procedure', 'likelihood', 'carlo', 'random', 'bootstrap', 'computer-based', 'computer-based', 'assigning', 'varian', 'generally', 'statistical', 'statistical', 'functional', 'generating', 'congruence', 'random', 'generating', 'simple', 'elegant', 'elementary', 'seeks', 'carlo', 'net', 'carlo', 'quasirandom', 'determining', 'fitting', 'plotting', 'simultaneously', 'correlation', 'difference', 'sample', 'histogram', 'displaying', 'displaying', 'testing', 'distribution', 'finding', 'distribution')
multiperfect	('distribution', 'number')
rounding	('class', 'quantity', 'precision', 'significance')
correspond	('limit', 'actual', 'form', 'probability')
actual	('correspond', 'dice', 'set', 'quantity', 'value', 'estimator', 'thickness', 'interpretations', 'minimize', 'error', 'vertical', 'converges', 'function', 'getting', 'matrix', 'observing', 'combination', 'state', 'results', 'distribution', 'expected')
falling	('data', 'total', 'within', 'point', 'sequence', 'element', 'within', 'point', 'bin', 'path', 'ball')
actually	('value', 'fall', 'cream--are', 'finite', 'existing', 'parameter', 'estimated', 'argument', 'contained', 'net', 'closed', 'average', 'predict')
ends	('binned', 'class')
sheppard	('histogram', 'correction', 'moment', 'correction', 'et', 'correction', 'chart', 'correction')
correction	('sheppard', 'bessel', 'factor', 'p', 'factor', 'bessel', 'sheppard', 'skewness', 'applied', 'sheppard', 'sheppard', 'stem', 'bonferroni', 'multiple-comparison', 'multiple-comparison', 'several', 'bonferroni', 'statistical', 'bonferroni', 'estimate', 'statistical', 'performed', 'multiple', 'bonferroni', 'chi', 'discrete', 'continuity', 'discrete')
specify	('value', 'class', 'general')
midvalue	('mark', 'central')
denoted	('p', 'class', 'interval', 'cumulative', 'boundary', 'cumulative', 'quantile', 'evans', 'quartile', 'other', 'similarly', 'data', 'p', 'median', 'variable', 'single', 'parameter', 'bernoulli', 'function', 'using', 'probability', 'fourier', 'parameter', 'th', 'variate', 'covariance', 'kurtosis', 'pearson', 'p', 'abramowitz', 'mean', 'moment', 'moment', 'second', 'ci', 'following', 'matrix', 'multivariate', 'p', 'special', 'occurred', 'subset', 'marginal', 'event', 'because', 'range', 'evans', 'quantile', 'probability', 'element', 'probabilities', 'range', 'evans', 'quantile', 'probability', 'value', 'variate', 'step', 'first', 'coefficient', 'correlation', 'one', '*', 'p', 'sample', 'second', 'f', 'parameter', 'distribution', 'function', 'evans', 'over', 'evans')
two-way	('table', 'frequency')
tabular	('table', 'mechanism')
mechanism	('tabular', 'least')
least	('mechanism', 'two', 'frequency', 'tests', 'performing', 'squares', 'histogram', 'squares', 'part', 'significant', 'deviation', 'coefficient', 'people', 'chance', 'chance', 'two', 'probability', 'coincident', 'probability', 'one', 'land', 'one', 'intersects', 'one', 'accurate', 'picked', 'getting', 'one', 'probability', 'one', 'throwing', 'one', 'three', 'two', 'likely', 'one', 'rolled', 'two', 'rolled', 'three', 'random', 'one', 'two', 'quality', 'linear', 'covariance', 'linear', 'linear', 'nonlinear', 'linear', 'vertical', 'error', 'interpolation', 'exponential', 'logarithmic', 'offsets', 'polynomial', 'nonlinear', 'applying', 'computed', 'regression', 'fitting', 'logarithmic', 'coefficient', 'fitting', 'regression', 'fitting', 'exponential', 'extended', 'regression', 'matrix', 'solution', 'regression', 'form', 'coefficient', 'regression', 'fitting', 'exponential', 'regression', 'fitting', 'regression', 'fitting', 'nonlinear', 'regression', 'length', 'inverse', 'regression', 'nonlinear', 'nonlinear', 'nonlinear', 'regression', 'regression', 'nonlinear', 'fractal', 'nonlinear', 'linear', 'coefficient', 'level', 'statistic', 'significant', 'likely', 'one', 'table', 'successes', 'uspensky', 'probability', 'successes', 'value', 'great')
rows	('two', 'two', 'arranged', 'two', 'five')
columns	('two', 'five', 'counting')
present	('statistics', 'categorical', 'future', 'up', 'time', 'appear', 'data', 'structure', 'expected', 'data')
categorical	('present', 'tests', 'variable', 'two')
precisely	('contingency', 'variance', 'fisher', 'order', 'indicate', 'noting', 'univariate', 'located', 'above')
contingency	('precisely', 'table', 'column', 'table', 'above', 'table', 'presented', 'table', 'using', 'data', 'table', 'test', 'statistics', 'table', 'test', 'table', 'test', 'table', 'association')
frequencies	('observed', 'arranged', 'expected', 'ability', 'expected', 'occurrence', 'limit', 'class', 'rescaled', 'class', 'observed', 'quantity')
arranged	('frequencies', 'rows', 'list', 'specified', 'nails', 'staggered')
intersection	('row', 'cell', 'column', 'event', 'line', 'place', 'empty')
row	('intersection', 'column', 'summary', 'column', 'summary', 'column', 'formula', 'composed', 'adding', 'cell', 'two', 'zero', 'multiplied', 'elementary', 'operations', 'placed', 'next', 'calculate', 'column', 'particular', 'column', 'consistent', 'column', 'obtain', 'repeated', 'second', 'numbered', 'bottom', 'hitting')
column	('row', 'contingency', 'row', 'summaries', 'intersection', 'row', 'elements', 'additional', 'added', 'five', 'central', 'oeis', 'elementary', 'operations', 'diagram', 'unique', 'digit', 'placed', 'appropriate', 'sorted', 'row', 'row', 'row')
five	('rows', 'columns', 'column', 'through', 'needle-tossing', 'independent', 'magazine', 'articles')
counting	('columns', 'header', 'dimensional', 'process', 'processes', 'processes', ';', 'number')
header	('counting', 'results')
sample	('random', 'adults', 'probability', 'statistics', 'shown', 'gini', 'symmetry', 'statistic', 'size', 'ordered', 'individual', 'lorenz', 'statistic', 'random', 'hogg', 'relationship', 'frequency', 'quantile', 'same', 'drawn', 'statistic', 'divide', 'range', 'closest', 'divide', 'range', 'divide', 'quartile', 'random', 'hogg', 'depend', 'size', 'population', 'random', 'hogg', 'range', 'mean', 'contained', 'deviation', 'example', 'polykay', 'central', 'moment', 'mean', 'mean', 'variance', 'term', 'central', 'mathstatica', 'first', 'mean', 'th', 'central', 'population', 'kenney', 'skewness', 'kurtosis', 'polykay', 'central', 'deviation', 'standard', 'th', 'central', 'moment', 'moment', 'size', 'first', 'central', 'first', 'central', 'moment', 'central', 'moment', 'moment', 'mean', 'mean', 'raw', 'moment', 'variance', 'mean', 'estimator', 'mean', 'relationship', 'skewness', 'mean', 'mean', 'mean', 'central', 'moment', 'raw', 'moment', 'size', 'size', 'variance', 'variance', 'second', 'central', 'moment', 'mean', 'variance', 'elements', 'estimated', 'need', 'taken', 'observed', 'variance', 'definition', 'variance', 'unbiased', 'variance', 'estimator', 'variance', 'moment', 'moment', 'central', 'moment', 'mean', 'mean', 'size', 'size', 'variance', 'computation', 'variance', 'value', 'kenney', 'formula', 'variance', 'variance', 'moment', 'central', 'variate', 'data', 'square', 'mean', 'mean', 'dist', 'variance', 'mean', 'moment', 'raw', 'th', 'raw', 'moment', 'moment', 'size', 'raw', 'smith', 'raw', 'mathstatica', 'raw', 'moment', 'moment', 'central', 'moment', 'mean', 'computing', 'set', 'last', 'th', 'bias-corrected', 'variance', 'first', 'definition', 'term', 'variance', 'moment', 'moment', 'variance', 'variance', 'variance', 'taken', 'moment', 'variance', 'value', 'variance', 'variance', 'varying', 'variance', 'distribution', 'distribution', 'variance', 'variance', 'variance', 'population', 'root', 'value', 'standard', 'deviation', 'standard', 'distribution', 'variance', 'variance', 'variance', 'standard', 'taken', 'moment', 'variance', 'variance', 'variance', 'error', 'error', 'size', 'standard', 'deviation', 'error', 'mean', 'first', 'distribution', 'computed', 'mean', 'necessary', 'distinction', 'bias-corrected', 'variance', 'variance', 'elements', 'estimated', 'need', 'k', 'moment', 'variance', 'variance', 'variance', 'computation', 'variance', 'wishart', 'accuracy', 'estimation', 'distribution', 'set', 'number', 'estimate', 'number', 'approximately', 'size', 'depend', 'statistic', 'size', 'set', 'probability', 'space', 'occurrence', 'configuration', 'probability', 'space', 'axioms', 'event', 'probability', 'space', 'informally', 'space', 'sigma-algebra', 'space', 'sigma-algebra', 'space', 'example', 'space', 'tt', 'space', 'variable', 'sigma', 'less', 'odd', 'even', 'coefficient', 'phenomenon', 'correlation', 'data', 'poor', 'method', 'random', 'interval', 'real', 'variance', 'drawn', 'variance', 'drawn', 'deviation', 'expectation', 'exact', 'value', 'cumulative', 'normalized', 'd-statistic', 'pair', 'space', 'space', 'experiment', 'space', 'subset', 'determined', 'determined', 'central', 'moment', 'raw', 'moment', 'mean', 'process', 'members', 'members', 'size', 'population', 'central', 'moment', 'mean', 'mean', 'proportion', 'proportion', 'raw', 'moment', 'size', 'size', 'space', 'space', 'variance', 'trial', 'proportion', 'ci', 'proportion', 'trial', 'size', 'evans', 'denoted', 'size', 'quantile', 'quantile', 'mean', 'mean', 'space', 'space', 'variance', 'number', 'members', 'members', 'normalized', 'efficiency', 'efficiency', 'size', 'proportion', 'same', 'distribution', 'mahalanobis', 'distribution', 'variance', 'random', 'infinite', 'mean', 'deviation', 'kind', 'mean', 'equal', 'mean', 'variance', 'successes', 'become', 'schum', 'outrageous', 'variable', 'mean')
adults	('sample', 'classified')
classified	('adults', 'two')
namely	('variables', 'gender', 'root', 'standard', 'value', 'denotes', 'size', 'square', 'relation', 'quantum', 'converse')
gender	('namely', 'favorite', 'case', 'favorite')
favorite	('gender', 'eat', 'gender', 'eat')
eat	('favorite', 'ice', 'prefer', 'ice', 'favorite', 'ice')
ice	('eat', 'cream', 'prefers', 'cream', 'prefers', 'cream', 'male', 'cream', 'eat', 'cream', 'eat', 'cream--are')
cream	('ice', 'larson', 'ice', 'ice', 'sandwiches', 'ice', 'sandwiches', 'ice', 'cup--is')
larson	('cream', 'farber', 'population', 'farber')
farber	('larson', 'one', 'larson', 'worth')
benefit	('one', 'data')
presented	('data', 'contingency', 'problem', 'striking', 'subject', 'choice', 'doubled')
easily	('one', 'perform', 'most', 'unordered', 'type', 'identified', 'one', 'various', 'standard', 'shown', 'technique', 'generalized')
perform	('easily', 'basic', 'digit')
basic	('perform', 'probability', 'test', 'assumption', 'ito', 'theory', 'follow', 'quantum')
calculations	('feat',)
feat	('calculations', 'easier')
easier	('feat', 'still', 'allow', 'computation', 'probabilities', 'using', 'devices', 'coefficient', 'test', 'determination')
augmenting	('still', 'summary')
summary	('augmenting', 'row', 'adding', 'row', 'ratio', 'statistic', 'coefficient', 'statistic')
total	('above', 'distribution', 'absolute', 'falling', 'equality', 'amount', 'curve', 'triangular', 'large', 'number', 'divided', 'number', 'frequency', 'number', 'precision', 'number', 'precision', 'number', 'order', 'statistic', 'probability', 'collected', 'coin', 'probability', 'probability', 'out', 'number', '?', 'probability', 'probability', 'example', 'distinct', 'a086265', 'number', 'boundaries', 'number', 'proportional', 'respectively', 'sum', 'out', 'successful', 'number', 'combining', 'over')
extended	('table', 'version', 'zhu', 'model', 'problem', 'shape', 'definition', 'naturally', 'least', 'crossbars', 'variation')
version	('extended', 'first', 'parametrized', 'quantile', 'wolfram', 'wolfram', 'wolfram', 'equivalent', 'cluster-based', 'viewed', 'univariate', 'modified', 'blom', 'modified', 'game', 'modified')
adding	('table', 'summary', 'row', 'one', 'obtain', 'obtain', 'obtain', 'respectively', 'subtracting')
summaries	('column', 'allow')
allow	('summaries', 'easier', 'cover', 'viewing')
person	('probability', 'probability', 'prefers', 'sandwiches', 'male', 'probability', 'male', 'arbitrary', 'second', 'birthday', 'third', 'birthday')
sampled	('prefers', 'waveform', 'uniformly')
prefers	('sampled', 'ice', 'person', 'ice')
cup	('probability',)
participant	('random', 'female')
female	('participant', 'what')
what	('female', 'computing', 'indicate', 'error', 'under', 'conditions', 'seeing', 'proportion', 'meaning', 'properly', 'form', 'identify', 'most', 'experimenter', 'most', 'experimenter')
computing	('what', 'conditional', 'formula', 'value', 'benefits', 'expected', 'cell', 'size', 'number', 'before', 'line', 'method', 'position', 'programs', 'sample', 'formula', 'small', 'matrix', 'other', 'computed', 'raw')
conditional	('computing', 'male', 'probability', 'test', 'probability', 'processes', 'probability', 'markoff', 'distribution', 'equal', 'distribution', 'process', 'intensity', 'zhu', 'intensity', 'processes', 'intensity', 'counterparts', 'intensity', 'intensity', 'analysis', 'intensity', 'specifies', 'expectation', 'set', 'probability', 'probability', 'intensity', 'time', 'intensity', 'probability', 'plugging', 'probability', 'probability', 'probability', 'probability', 'iff', 'theorem', 'probability', 'analysis', 'intensity', 'analysis', 'intensity', 'probability', 'probability', 'event', 'set', 'theorem', 'probability', 'specifying', 'specifying', 'intensity', 'event', 'theorem', 'probability', 'mean', 'expectation', 'logit', 'choice-specific', 'logit', 'regression', 'expectation', 'calculate', 'calculate', 'parameter')
probabilities	('easier', 'summarizes', 'future', 'determined', 'kenney', 'unions', 'individual', 'pp', 'needle', 'investigated', 'triangular', 'him', 'set', 'frequentists', 'denoted', 'obey', 'point', 'point', 'event', 'sum', 'asymptotically', 'various', 'sum', 'one', 'added', 'outcome', 'been', 'independent', 'satisfy', 'various', 'various', 'example', 'correct', 'sum', 'ratio', 'poisson')
sandwiches	('cream', 'person', 'cream', 'preferred')
male	('person', 'conditional', 'person', 'ice')
preferred	('sandwiches', 'other')
other	('preferred', 'common', 'denoted', 'far', 'no', 'unbiased', 'compared', 'unbiased', 'compared', 'unbiased', 'past', 'fitting', 'standard', 'obtain', 'several', 'still', 'authors', 'process', 'cluster-based', 'independent', 'liniger', 'authors', 'abramson', 'honsberger', 'vere-jones', 'authors', 'stationarity', 'pawlas', 'schoenberg', 'within', 'two', 'distribution', 'space', 'specified', 'one', 'coefficient', 'two', 'moment', 'measured', 'number', 'slightly', 'typically', 'likelihood-ratio-test', 'longer', 'computing', 'possible', 'differ', 'significant', 'calls', 'closely', 'statistical', 'et', 'functional', 'block', 'discrete', 'starting', 'two')
analyses	('statistical', 'performed')
performed	('analyses', 'data', 'tedious', 'transpositions', 'rate', 'test', 'simultaneously', 'simplest', 'test', 'correction', 'variate')
useful	('one', 'value', 'bracket', 'descriptive', 'covariance', 'looking', 'statistic', 'determining', 'unclear', 'formula', 'number', 'computational', 'extremely', 'computational', 'distribution', 'testing', 'case', 'consequence')
know	('value', 'expected', 'quantity', 'plotting')
cell	('frequency', 'intersection', 'expect', 'expected', 'computing', 'expected', 'half', 'row', 'diagonally')
formula	('row', 'computing', 'absolute', 'sample', 'somtimes', 'hoc', 'lacking', 'approximately', 'supposedly', 'useful', 'practice', 'slovin', 'lacks', 'slovin', 'nonparametric', 'explicit', 'regularized', 'mosteller', 'oeis', 'using', 'summarized', 'kac', 'random', 'ito', 'hudson', 'expressing', 'computing', 'uncorrelated', 'linear', 'using', 'beautiful', 'calculate', 'bowley', 'statistical', 'statistical', 'spencer', 'spencer', 'average', 'written', 'spencer', 'time', 'slovin', 'statistical', 'noncentral', 'paradox', 'first', 'central', 'connecting')
expect	('one', 'cell', 'room')
men	('number', 'who')
who	('men', 'prefer', 'gauss', 'connection', 'moser', 'people', 'et', 'collected', 'pascal', 'solved')
prefer	('who', 'eat', 'smith', 'zwillinger', 'definition', 'pp', 'distribution')
cup--is	('cream', 'approximately')
approximately	('cup--is', 'whereby', 'position', 'unbiased', 'always', 'last', 'sample', 'formula', 'missed', 'proofreading', 'duck', 'extant', 'variable', 'normal', 'factorial', 'normal', 'fall', 'large', 'normal', 'variate', 'log', 'effect', 'normally')
whereby	('approximately', 'one', 'equation', 'one')
deduce	('one', 'somehow')
somehow	('deduce', 'particular')
particular	('somehow', 'demographic', 'time', 'pair', 'et', 'meaning', 'gets', 'very', 'probability', 'sense', 'defining', 'applied', 'importance', 'chance', 'event', 'spatial-temporal', 'indicate', 'subject', 'reference', 'type', 'probability', 'ordered', 'inverse', 'type', 'model', 'choice', 'done', 'matrix', 'row', 'one', 'usage', 'statistical', 'independent')
demographic	('particular', 'included')
included	('demographic', 'leading')
too	('knowing', 'inches', 'inches', 'difference', 'inches', 'inches')
knowing	('too', 'automatically', 'arithmetic', 'stop', 'without', 'loosely', 'student')
automatically	('knowing', 'without')
without	('automatically', 'repeated', 'done', 'knowing', 'payoff', 'account', 'processes', 'range', 'loss', 'variable', 'reference', 'parameter', 'resorting', 'object', 'function', 'numerical', 'fit')
repeated	('without', 'application', 'procedure', 'up', 'process', 'cards', 'equivalent', 'picking', 'row', 'taken', 'four', 'procedure', 'eight')
application	('repeated', 'one', 'language', 'package', 'mathematica', 'package', 'mathematica', 'package', 'mathematica', 'package', 'mathematica', 'package', 'mathematica', 'package', 'mathematica', 'package', 'mathematica', 'package', 'mathematica', 'package', 'mathematica', 'package', 'mathematica', 'package', 'mathematica', 'package', 'combines', 'example')
major	('one', 'benefits', 'chunks', 'difficulty', 'cramer', 'index')
benefits	('major', 'computing')
ability	('frequencies', 'test')
test	('ability', 'two', 'common', 'common', 'contingency', 'proportions', 'form', 'chi-squared', 'several', 'squared', 'conditional', 'contingency', 'proportions', 'statistical', 'contingency', 'r', 'rank', 'robust', 'robust', 'anova', 'resampling', 'nonparametric', 'alternative', 'paired', 'basic', 'sum', 'sign', 'statistical', 'hypothesis', 'nonparametric', 'sign', 'assumes', 'wilcoxon', 'rank', 'statistical', 'fisher', 'sign', 'hypothesis', 'parametric', 'wilcoxon', 'wilcoxon', 'statistic', 'statistical', 'tail', 'sphere', 'randomness', 'making', 'wilcoxon', 'rank', 'rank', 'statistical', 'kolmogorov', 'smirnov', 'r', 'statistical', 'wilcoxon', 'rank', 'rank', 'spearman', 'sum', 'wilcoxon', 'rank', 'zipf', 'easier', 'two', 'agreement', 'two', 'bland', 'confidence', 'hypothesis', 'hypothesis', 'anova', 'kolmogorov', 'smirnov', 'kuiper', 'heterogeneity', 'random', 'factor', 'anova', 'student', 'performed', 'hypotheses', 'individual', 'critical', 'alpha', 'statistical', 'using', 'fit', 'squared', 'statistical', 'chi', 'significance', 'determination', 'equality', 'exact', 'unique', 'use', 'normal', 'exact', 'statistical', 'nonrandom', 'either', 'table', 'most', 'p-value', 'computed', 'exact', 'statistical', 'hotelling', 'statistical', 'hotelling', 'alternative', 'identify', 'probability', 'statistic', 'alpha', 'sign', 'hypothesis', 'statistical', 'statistical', 'statistical', 'statistic', 'rank', 'goodness-of-fit', 'statistical', 'distribution', 'fact', 'calculate', 'form', 'smirnov', 'statistical', 'anderson', 'anderson', 'quantity', 'nested', 'medicine', 'nonnested', 'negative', 'single', 'statistic', 'anova', 'medicine', 'nonnested', 'likelihood', 'log', 'alternative', 'statistic', 'paired', 'statistical', 'fisher', 'sign', 'hypothesis', 'rank', 'parametric', 'statistical', 'probability', 'true', 'true', 'probability', 'false', 'false', 'sensitivity', 'statistical', 'estimator', 'positive', 'specificity', 'statistical', 'type', 'alpha', 'significance', 'statistical', 'statistical', 'determining', 'significance', 'statistical', 'significance', 'statistical', 'alpha', 'negative', 'negative', 'sensitivity', 'statistical', 'type', 'alternative', 'positive', 'should', 'predictive', 'statistical', 'statistical', 'statistical', 'positive', 'statistic', 'probability', 'negative', 'negative', 'observed', 'several', 'performed', 'statistical', 'statistical', 'anova', 'squared', 'fisher', 'exact', 'fisher', 'sign', 'kolmogorov', 'smirnov', 'likelihood', 'parametric', 'predictive', 'significance', 'specificity', 'sum', 'wilcoxon', 'rank', 'false', 'null', 'statistical', 'type', 'true', 'null', 'statistical', 'type', 'determination', 'equality', 'attributes', 'smirnov', 'logit')
examined--in	('variables',)
case	('gender', 'problem', 'fit', 'special', 'maximum', 'transformations', 'special', 'simple', 'probability', 'special', 'covariance', 'iterating', 'even', 'special', 'power', 'appropriate', 'singular', 'kenney', 'special', 'analytically', 'intensity-based', 'authors', 'symmetric', 'nonzero', 'special', 'analytically', 'extreme', 'probability', 'variance', 'estimator', 'variance', 'game', 'square', 'clean', 'satisfies', 'probability', 'special', 'random', 'last', 'most', 'collection', 'find', 'above', 'special', 'racs', 'life', 'revolver', 'killed', 'revolver', 'homogeneous', 'probability', 'quasirandom', 'simplest', 'uncorrelated', 'derived', 'reasonable', 'vs', 'analyzing', 'error', 'matrix', 'three', 'special', 'general', 'general', 'special', 'sequence', 'important', 'chebyshev', 'limiting', 'one', 'table', 'statistically', 'uniseriate', 'assess', 'multivariate', 'optimal', 'special', 'erlang', 'special', 'log', 'mean', 'cauchy', 'general', 'gibrat', 'noncentral', 'special', 'special', 'doubly', 'limiting', 'discrete', 'large', 'normal', 'simplifies', 'normal', 'special', 'chi-squared', 'distribution', 'intermediate', 'i', 'iv', 's', 'distribution', 'first', 'special', 'equal', 'general', 'steinhaus', 'odd', 'excess', 'distribution', 'excess', 'characteristic', 'definition', 'equivalent', 'useful', 'statistical')
cream--are	('ice', 'actually')
independent	("they've", 'distribution', 'occur', 'random', 'definition', 'sequence', 'probability', 'completely', 'type', 'statistically', 'function', 'moment', 'moment-generating', 'two', 'normal', 'random', 'assumed', 'one', 'immigrants', 'immigrants', 'distributed', 'random', 'cluster', 'other', 'correlation', 'principle', 'five', 'series', 'expression', 'coefficient', 'statistically', 'statistically', 'statistically', 'true', 'probability', 'hold', 'function', 'entries', 'taken', 'coefficient', 'distributed', 'correlation', 'entries', 'taken', 'no', 'constant', 'random', 'brownian', 'condition', 'brownian', 'motion', 'coefficient', 'origin', 'function', 'variable', 'function', 'variable', 'appear', 'tosses', 'variance', 'several', 'statistical', 'difference', 'identically', 'covariance', 'covariance', 'experiment', 'event', 'probabilities', 'papoulis', 'event', 'particular', 'variance', 'two', 'unbiased', 'distribution', 'random', 'parameter', 'random', 'two', 'identically-distributed', 'identically-distributed', 'two', 'normal', 'ratio', 'normally', 'distributed', 'sum', 'normally', 'delta', 'normally', 'distributed', 'chose', 'distributed', 'sequence', 'bernoulli', 'mean', 'binomial', 'variable', 'interval', 'variable', 'random', 'sequence', 'random', 'square', 'normal', 'freedom', 'converse', 'distribution', 'random', 'mutually', 'random', 'sequence', 'identically')
they've	('independent', 'been')
assumed	('been', 'function', 'independent', 'existence', 'birthdays', 'uniform', 'space', 'value', 'arbitrary', 'set', 'set', 'event', 'form', 'distribution', 'condition', 'equivalently')
throughout	('done', 'roles', 'various', 'uniform', 'year', 'function', 'various')
done	('throughout', 'computation', 'fixed', 'been', 't', 'without', 'computation', 'difficult', 'only', 'one', 'sum', 'symbolically', 'particular', 'first', 'cannot', 'closed', 'integral')
comparing	('frequency', 'observed', 'occur')
performing	('frequency', 'chi-squared', 'diagram', 'least', 'variable', 'matrix', 'same', 'matrix', 'same', 'first', 'two')
chi-squared	('performing', 'form', 'test', 'instance', 'testing', 'distribution', 'distribution', 'quantity', 'distribution', 'value', 'root', 'random', 'function', 'distribution', 'noncentral', 'includes', 'noncentral', 'distribution', 'noncentral', 'case', 'promised', 'variable', 'variable', 'variance')
homogeneity	('table', 'proportions', 'proportions')
proportions	('homogeneity', 'test', 'several', 'equal', 'homogeneity', 'test')
form	('test', 'chi-squared', 'either', 'normalized', 'fourth', 'variance', 'wolfram', 'unwieldy', 'skewness', 'explicit', 'characteristic', 'intensity', 'history', 'function', 'bacry', 'functional', 'functional', 'fit', 'functional', 'estimation', 'parametric', 'process', 'space', 'written', 'correspond', 'subintervals', 'discrete', 'kostlan', 'equation', 'cut', 'spanning', 'subintervals', 'term', 'montroll', 'equation', 'interpreted', 'equation', 'take', 'unitary', 'equation', 'what', 'model', 'analytic', 'fitting', 'applied', 'linear', 'linearized', 'function', 'matrix', 'simpler', 'defining', 'functional', 'take', 'analytic', 'fitting', 'minimum', 'unwieldy', 'best-fit', 'matrix', 'vandermonde', 'least', 'common', 'linear', 'linear', 'transform', 'block', 'analytic', 'component', 'applying', 'residual', 'term', 'asymptotic', 'bernoulli', 'polynomial', 'bonferroni', 'respectively', 'test', 'concatenated', 'sequence', 'assumed', 'borel', 'function', 'multivariate', 'correlation', 'closed', 'small', 'similar', 'solution', 'using', 'papoulis', 'normalized', 'cumulative', 'standard', 'weighted', 'variate', 'multivariate', 'student', 'closed', 'uspensky', 'mean', 'different', 'distribution', 'variance', 'weibull', 'distribution', 'distribution', 'represented', 'functional', 'universe', 'distribution', 'joint', 'work', 'range', 'normal', 'variate', 'normal', 'fourier', 'quadratic', 'distributed')
population	('larson', 'gini', 'infinite', 'individual', 'word', 'number', 'purely', 'hypothetically', 'completely', 'mathematically', 'descriptive', 'mean', 'sample', 'median', 'median', 'estimator', 'standard', 'estimator', 'mean', 'unbiased', 'sample', 'taken', 'size', 'estimator', 'mean', 'variance', 'skewness', 'kurtosis', 'estimator', 'standard', 'point', 'term', 'central', 'estimator', 'mean', 'mean', 'estimate', 'estimator', 'l', 'taken', 'function', 'mean', 'distribution', 'mean', 'estimator', 'mean', 'mean', 'mean', 'variance', 'estimator', 'raw', 'taken', 'central', 'estimator', 'normal', 'sample', 'taken', 'normal', 'based', 'estimator', 'mean', 'distribution', 'mean', 'written', 'value', 'variance', 'estimator', 'estimator', 'estimate', 'sampling', 'unknown', 'characteristic', 'size', 'depend', 'variability', 'value', 'comparison', 'coefficient', 'correlation', 'freedom', 'regression', 'ratio', 'correlation', 'common', 'technique', 'error', 'comparison', 'yearly', 'observation', 'number', 'through', 'trial', 'sample', 'sampling', 'analysis', 'true', 'value', 'measurement', 'estimator', 'standard', 'mean', 'bernoulli', 'bernoulli', 'estimator', 'mean', 'mean', 'function', 'infinite', 'mean', 'kenney', 'equal')
worth	('farber', 'noting', 'time', 'term')
above-mentioned	('noting',)
testing	('chi-squared', 'randomly-selected', 'hypothesis', 'hypothesis', 'paired', 'hypothesis', 'significance', 'hypothesis', 'p', 'contrary', 'hypothesis', 'null', 'hypothesis', 'statistical', 'hypothesis', 'monster', 'hypothesis', 'use', 'hypothesis', 'four', 'hypothesis', 'statistical', 'method', 'nested', 'procedure', 'equality', 'hypothesis', 'hypothesis', 'student', 'hypothesis', 'null', 'distribution', 'two', 'useful', 'two')
randomly-selected	('testing', 'sampling')
sampling	('randomly-selected', 'observed', 'results', 'population', 'random', 'study', 'theory', 'phenomenon', 'ghost', 'number', 'variance', 'trial', 'statistic', 'selection', 'population', 'vital', 'infinite-precision', 'band-limited', 'et', 'nyquist', 'size', 'theorem')
tests	('least', 'play', 'statistical', 'categorical')
play	('tests', 'important', 'fact', 'extremely', 'fact')
important	('play', 'roles', 'estimate', 'part', 'deviation', 'descriptive', 'maximum', 'very', 'generalized', 'extremely', 'role', 'proof', 'prime', 'theory', 'modeling', 'coefficient', 'physical', 'most', 'case', 'particularly', 'statistical')
roles	('important', 'throughout')
various	('throughout', 'branches', 'easily', 'statistical', 'throughout', 'subfields', 'above', 'count', 'up', 'probabilities', 'classes', 'names', 'plot', 'equal', 'probabilities', 'probabilities', 'small')
branches	('various',)
variable	('categorical', 'chi', 'statistics', 'expected', 'random', 'function', 'denoted', 'probability', 'continuous', 'expectation', 'multiple', 'mean', 'expectation', 'random', 'number', 'index', 'correlated', 'always', 'cumulant-generating', 'rewrite', 'obtain', 'probability', 'performing', 'variance', 'identical', 'variance', 'opposed', 'below', 'distributed', 'distribution', 'opposed', 'joint', 'theorem', 'probability', 'opposed', 'lehmann', 'approximation', 'probability', 'probability', 'line', 'binomial', 'always', 'random', 'probability', 'random', 'random', 'obey', 'find', 'random', 'state', 'random', 'random', 'sample', 'strictly', 'probability', 'random', 'schrage', 'random', 'measurable', 'random', 'real', 'random', 'random', 'random', 'variate', 'generated', 'random', 'variate', 'random', 'stochastic', 'probability', 'random', 'state', 'without', 'obey', 'random', 'random', 'variate', 'increments', 'random', 'random', 'identical', 'averaging', 'random', 'random', 'value', 'distribution', 'approximately', 'independent', 'independent', 'value', 'multiple', 'function', 'tabulated', 'general', 'variance', 'examine', 'identically', 'two-dimensional', 'exist', 'observed', 'random', 'random', 'random', 'uncorrelated', 'over', 'distribution', 'take', 'erlang', 'joint', 'joint', 'theorem', 'logarithm', 'normal', 'levy', 'logarithm', 'normal', 'results', 'product', 'same', 'results', 'sum', 'probability', 'applies', 'distributed', 'scheffe', 'fisher-behrens', 'expectation', 'weighted', 'random', 'satisfies', 'random', 'chi-squared', 'random', 'chi-squared', 'random', 'very', 'random', 'beta', 'characterized', 'take', 'product', 'order', 'random', 'possible', 'independent', 'poisson', 'connecting', 'distributed', 'joint', 'independent', 'memoryless', 'distribution', 'description', 'random', 'new', 'sample')
chi	('variable', 'squared', 'pp', 'squared', 'test', 'squared', 'correction', 'squared', 'distribution', 'distribution', 'distribution', 'excess', 'distribution', 'distribution', 'squared', 'distribution', 'squared', 'distribution', 'distribution', 'inverse', 'squared', 'noncentral', 'squared', 'distribution', 'distribution', 'distribution', 'squared', 'distribution', 'squared', 'distribution', 'squared', 'noncentral', 'squared', 'distribution', 'squared', 'distribution', 'squared', 'theorem', 'squared')
squared	('chi', 'test', 'mean', 'deviation', 'mean', 'deviation', 'sum', 'sum', 'sum', 'mean', 'chi', 'test', 'chi', 'distribution', 'chi', 'test', 'chi', 'distribution', 'chi', 'distribution', 'chi', 'distribution', 'chi', 'distribution', 'chi', 'distribution', 'chi', 'distribution', 'chi', 'distribution', 'chi', 'distribution', 'chi', 'distribution', 'chi', 'distribution', 'chi', 'distribution')
occurrence	('frequencies', 'event', 'consisting', 'finite', 'refers', 'future', 'density', 'sample', 'marking', 'exclusive', 'one', 'processes', 'over', 'revealed', 'realization', 'self-correcting', 'past', 'inhibits', 'future', 'self-exciting', 'past', 'point', 'future', 'experiment', 'tossing')
upper	('frequency', 'boundary', 'lower', 'function', 'incomplete', 'over', 'finch', 'bound', 'statistic', 'triangular', 'against', 'class', 'median', 'lower', 'driven', 'middle')
boundary	('upper', 'class', 'denoted', 'probability', 'polygon', 'necessary', 'class')
less	('value', 'size', 'lorenz', 'deviate', 'followed', 'extreme', 'median', 'efficient', 'mean', 'sensitive', 'value', 'down', 'frequent', 'quantities', 'equal', 'quantities', 'equal', 'somewhat', 'optimal', 'natural', 'frequently', 'length', 'shortest', 'diameter', 'probability', 'string', 'expected', 'seeing', 'gardner', 'somewhat', 'revolver', 'walk', 'unity', 'sample', 'greater', 'one', 'oeis', 'sum', 'equal', 'because', 'hypothesis', 'conservative', 'function', 'widely', 'variate', 'value', 'equal')
polygon	('frequency', 'frequency', 'frequency', 'descriptive', 'curve', 'joining', 'generalized', 'boundary', 'perimeter', 'uspensky', 'overlap', 'avoiding', 'self', 'staircase', 'three', 'frequency', 'statistical', 'frequency', 'ogive', 'frequency', 'gaussian', 'frequency', 'ogive', 'frequency', 'histogram')
quantile	('frequency', 'rank', 'quartile', 'sample', 'evaluating', 'function', 'rank', 'rank', 'rank', 'plot', 'word', 'no', 'denoted', 'ties', 'function', 'version', 'definition', 'common', 'th', 'observation', 'estimate', 'descriptive', 'paper', 'function', 'function', 'function', 'plot', 'percentile', 'quartile', 'denoted', 'function', 'function', 'defining', 'defines', 'function', 'range', 'function', 'function', 'random', 'denoted', 'experiment', 'random', 'plot', 'plot', 'plot', 'statisticalplots`', 'statisticalplots`', 'plot', 'position', 'trial', 'sample', 'sample')
factor	('statistics', 'level', 'correction', 'relationship', 'correction', 'probably', 'multiplicative', 'multiplicative', 'along', 'spherical', 'additional', 'behind', 'within', 'within', 'same', 'within', 'test', 'level', 'same', 'extra', 'added', 'normalization', 'abramowitz')
level	('factor', 'descriptive', 'initial', 'eckhardt', 'treatment', 'anova', 'sum', 'mean', 'mean', 'factor', 'least', 'treatment', 'significance', 'two', 'alpha')
phrase	('tukey', 'poll')
tukey	('phrase', 'data', 'fence', 'calls', 'minitab', 'hoaglin', 'introduced', 'rose', 'et', 'trimean', 'plot', 'mean-difference', 'create', 'convention', 'original', 'hinge', 'addition', 'original', 'figure;', 'labels', 'p', 'additional', 'stem-and-leaf', 'mean')
outside	('point', 'outer', 'step', 'steps', 'value', 'outer', 'lie', 'overall', 'exponential', 'inner')
outer	('outside', 'hinges', 'outside', 'forming', 'product', 'twice', 'product', 'function', 'one', 'exponential')
far	('fence', 'out', 'fence', 'point', 'left', 'other')
step	('outside', 'range', 'h-spread', 'descriptive', 'taken', 'equally', 'discrete', 'randomly', 'directions', 'taken', 'equal', 'probability', 'probability', 'taken', 'taken', 'out', 'right', 'right', 'left', 'opposed', 'above', 'toward', 'following', 'sum', 'random', 'taken', 'absolute', 'unit', 'equally', 'unit', 'size', 'only', 'first', 'positive', 'oeis', 'first', 'positive', 'up', 'before', 'number', 'oeis', 'following', 'same', 'denoted', 'lattice', 'random', 'oeis', 'oeis', 'formulate', 'heaviside', 'heaviside', 'heaviside', 'heaviside', 'ball')
hinges	('inner', 'outer', 'same')
steps	('two', 'outside')
calls	('tukey', 'definition', 'other')
vector	('random', 'probability', 'initial', 'point', 'distribution', 'multivariate', 'elements', 'mean', 'covariance', 'mean', 'covariance', 'matrix', 'under', 'random', 'solution', 'setting', 'entries', 'two', 'f-distribution', 'gaussian')
continuous	('distribution', 'first', 'pp', 'uniform', 'single', 'variable', 'multiple', 'named', 'function', 'distribution', 'variate', 'distribution', 'whereas', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'integral', 'distribution', 'pdf', 'distribution', 'probability', 'distribution', 'function', 'strictly', 'discrete', 'probability', 'distribution', 'two-dimensional', 'uniform', 'transformation', 'variate', 'permutation', 'time', 'distribution', 'almost', 'holder', 'almost', 'space', 'treated', 'differentiable', 'function', 'segment', 'cumulative', 'distribution', 'distribution', 'cumulative', 'nearly', 'remove', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'approximate', 'distribution', 'variate', 'take', 'range', 'common', 'distribution', 'distribution', 'distribution', 'copula', 'coefficient', 'successes', 'theorem', 'distribution', 'distribution', 'distribution', 'distribution', 'analog', 'distribution', 'distribution', 'statistical', 'distribution', 'ratio', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'theorem', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'taken', 'uniform', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'solution', 'logistic', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'function', 'distribution', 'distribution', 'distribution', 'distribution', 'system', 'distribution', 'function', 'theorem', 'error', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'uniform', 'expected', 'distribution', 'uniform', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'term', 'distribution', 'distribution', 'function', 'probability', 'neither', 'using', 'you', 'equivalent', 'distribution', 'distribution', 'function', 'probability')
second	('first', 'order', 'contributes', 'measurement', 'written', 'sample', 'high', 'statistician', 'denoted', 'moment', 'pearson', 'coefficient', 'work', 'term', 'term', 'term', 'mean', 'raw', 'equal', 'central', 'term', 'central', 'equal', 'central', 'probability', 'person', 'probability', 'event', 'ways', 'occur', 'up', 'throw', 'high', 'statistician', 'bit', 'equal', 'domain', 'theorem', 'except', 'implication', 'part', 'function', 'variance', 'denoted', 'function', 'mean', 'moment', 'function', 'first', 'raw', 'function', 'function', 'nail', 'row', 'number')
order	('second', 'partial', 'multiplied', 'become', 'increasing', 'writing', 'theorem', 'statistic', 'minimum', 'statistic', 'statistical', 'mean', 'statistic', 'th', 'statistic', 'statistic', 'mean', 'statistical', 'mode', 'statistic', 'statistic', 'confidence', 'precisely', 'combinations', 'combinations', 'total', 'moment', 'statistic', 'binned', 'obtain', 'variance', 'obtain', 'formally', 'estimate', 'th', 'statistic', 'function', 'statistical', 'combinations', 'l-estimate', 'statistic', 'set', 'first', 'stationary', 'set', 'set', 'reversing', 'coordinate', 'detect', 'picking', 'generate', 'randomizes', 'large', 'random', 'become', 'travel', 'median', 'specified', 'differently', 'high-quality', 'value', 'weight', 'formulation', 'term', 'statistic', 'quantify', 'diagram', 'comparison', 'avoid', 'most', 'comparison', 'avoid', 'observation', 'estimate', 'extreme', 'distribution', 'statistic', 'p', 'explicitly', 'extreme', 'higher', 'raw', 'kind', 'distribution', 'term', 'smaller', 'lower', 'variable', 'combining', 'smallest')
partial	('order', 'function', 'function', 'derivative', 'residual', 'value')
derivatives	('fisher',)
fisher	('derivatives', 'information', 'entry', 'information', 'statistics', 'information', 'precisely', 'information', 'value', 'information', 'variance', 'estimator', 'point', 'rose', 'encountered', 'divide', 'sign', 'similar', 'sign', 'test', 'sign', 'cornish', 'asymptotic', 'coefficient', 'spearman', 'cornish', 'asymptotic', 'cornish', 'asymptotic', 'cornish', 'asymptotic', 'index', 'index', 'index', 'index', 'index', 'data', 'behrens', 'exact', 'one', 'looked', 'appearing', 'exact', 'estimate', 'sign', 'hypothesis', 'test', 'sign', 'test', 'exact', 'test', 'sign', 'distribution', 'gamma', 'tippett', 'mode', 'z', 'distribution', 'behrens', 'erfc', 'behrens', 'converse', 'theorem', 'theorem', 'defining', 'transformation')
information	('fisher', 'matrix', 'matrix', 'fisher', 'matrix', 'fisher', 'fisher', 'fisher', 'matrix', 'making', 'precision', 'returning', 'assumption', 'only', 'assumes', 'magnitudes', 'well;', 'based', 'inferred')
matrix	('information', 'information', 'th', 'information', 'descriptive', 'score', 'information', 'likelihood', 'likelihood', 'probability', 'probability', 'transition', 'substitution', 'markov', 'markov', 'characterize', 'elements', 'real', 'stochastic', 'square', 'entries', 'under', 'stochastic', 'markov', 'stochastic', 'horn', 'respectively', 'quantities', 'covariance', 'covariance', 'statistical', 'variance', 'covariance', 'error', 'covariance', 'joint', 'denoted', 'multivariatestatistics`', 'denotes', 'denotes', 'composed', 'vector', 'wishart', 'scale', 'multinormal', 'random', 'wigner', 'exist', 'variate', 'random', 'type', 'random', 'theory', 'real', 'edelman', 'random', 'derived', 'parity', 'dimension', 'trace', 'entries', 'real', 'denotes', 'spectral', 'random', 'random', 'complex', 'girko', 'integer', 'integer', 'random', 'real', 'wigner', 'stochastic', 'stochastic', 'number', 'variate', 'multivariate', 'large', 'entries', 'large', 'symmetric', 'random', 'random', 'expressing', 'characteristic', 'form', 'manova', 'inverse', 'penrose', 'inverse', 'form', 'obtain', 'least', 'transpose', 'vandermonde', 'moore-penrose', 'moore-penrose', 'type', 'meyer', 'use', 'nonsingular', 'performing', 'elementary', 'nonsingular', 'performing', 'transform', 'identity', 'rank', 'rank', 'et', 'inverse', 'inverse', 'inverse', 'penrose', 'inverse', 'pseudoinverse', 'moore-penrose', 'generalized', 'pseudoinverse', 'independently', 'inverse', 'wolfram', 'penrose', 'inverse', 'fitting', 'inverse', 'pseudoinverse', 'concise', 'quantities', 'standard', 'construct', 'technique', 'case', 'correlated', 'penrose', 'inverse', 'normal', 'penrose', 'inverse', 'normal', 'pseudoinverse', 'pseudoinverse', 'even', 'possible', 'moore-penrose', 'pseudoinverse', 'pseudoinverse', 'regression', 'inverse', 'inverse', 'inverse', 'penrose', 'inverse', 'projection', 'covariance', 'variance', 'entries', 'calculate', 'actual', 'particular', 'relevant', 'computing', 'redundancy', 'covariance', 'covariance', 'wishart', 'scale', 'correlation')
th	('matrix', 'entry', 'percentile', 'value', 'value', 'returns', 'order', 'q3', 'quantile', 'encountering', 'most', 'unique', 'sum', 'variance', 'sample', 'sample', 'denoted', 'denotes', 'central', 'raw', 'distribution', 'raw', 'zero', 'true', 'raw', 'sample', 'sample', 'interval', 'distribution', 'conditions', 'bernoulli', 'distribution', 'central', 'process', 'generation', 'reorder', 'order', 'through', 'mark', 'event', 'value', 'event', 'head', 'say', 'winning', 'toss', 'point', 'recording', 'moment', 'observation', 'polynomial', 'degree', 'value', 'length', 'group', 'observation', 'observation', 'function', 'raw', 'maximum', 'raw', 'first', 'central', 'time', 'poisson', 'time', 'poisson', 'time', 'poisson', 'function', 'raw', 'theta', 'raw', 'lambda', 'raw', 'sigma', 'raw', 'function', 'raw', 'lambda', 'raw', 'alpha', 'raw', 'first', 'central', 'vanishes', 'moment', 'raw', 'moment', 'before', 'hitting', 'peg', 'odd', 'selection', 'normalized', 'raw', 'success', 'rho', 'raw', 'theorem')
entry	('th', 'fisher')
tabulation	('raw',)
raw	('tabulation', 'data', 'moment', 'moment', 'moment', 'moment', 'sample', 'moment', 'sample', 'moment', 'moment', 'moment', 'term', 'term', 'moment', 'moment', 'generate', 'series', 'term', 'kurtosis', 'moment', 'th', 'moment', 'th', 'th', 'first', 'taken', 'value', 'mathstatica', 'moment', 'multivariate', 'mathstatica', 'moment', 'sample', 'moment', 'sample', 'moment', 'sample', 'population', 'sample', 'moment', 'sample', 'moment', 'moment', 'moment', 'second', 'p', 'moment', 'moment', 'sample', 'sample', 'moment', 'kind', 'th', 'th', 'normalized', 'moment', 'defining', 'th', 'th', 'first', 'th', 'relation', 'normalized', 'distribution', 'th', 'excess', 'th', 'th', 'first', 'before', 'computing', 'pp', 'th', 'moment', 'exist', 'th', 'second', 'order', 's', 'freedom', 'mean', 'differentiating', 'beta', 'sincich', 'function', 'first', 'normalized', 'first', 'th', 'function', 'p', 'th')
dividing	('data', 'quantities', 'through', 'coefficient', 'through')
elements	('data', 'fraction', 'specific', 'sample', 'priori', 'chain', 'matrix', 'sum', 'column', 'two', 'two', 'complete', 'sample', 'priori', 'data', 'partitioned', 'data', 'proximate', 'set', 'immigrants', 'vector')
fraction	('elements', 'out', 'binary', 'tile', 'tile', 'tile', 'tile', 'representation', 'colon', 'ratio', 'rational', 'mistakes', 'calling', 'binary', 'oeis', 'plot', 'function', 'proportion', 'identity', 'trial', 'acceptable')
pair	('within', 'class', 'possible', 'particular', 'complex-conjugated', 'complex', 'uniform', 'term', 'generating', 'digit', 'digit', 'element', 'mean', 'one', 'sample', 'number', 'probability')
discrete	('value', 'variate', 'single', 'multiple', 'take', 'deviation', 'distribution', 'example', 'uniform', 'named', 'distribution', 'uniform', 'similarly', 'value', 'distribution', 'value', 'sum', 'distribution', 'distribution', 'distribution', 'distribution', 'whereas', 'continuous', 'work', 'nature', 'distribution', 'distribution', 'distribution', 'localized', 'localized', 'spaced', 'set', 'theorem', 'discrepancy', 'class', 'subintervals', 'form', 'discrepancy', 'discrepancy', 'discrepancy', 'sequence', 'step', 'allowed', 'number', 'number', 'signal', 'correction', 'binomial', 'correction', 'coefficient', 'distribution', 'case', 'binomial', 'distribution', 'uniform', 'machine', 'distribution', 'simplest', 'other', 'distribution', 'distribution', 'distribution', 'probability', 'distribution', 'theorem', 'only', 'common', 'distribution', 'distribution', 'mean', 'distribution', 'distribution', 'uniform', 'function', 'uniform', 'distribution', 'uniform', 'a086112', 'uniform', 'distribution', 'distribution', 'distribution', 'distribution', 'board', 'distribution', 'distribution', 'analog', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'process', 'distribution', 'distribution', 'distribution', 'distribution', 'function', 'probability', 'joint', 'distribution', 'distribution', 'distribution', 'function', 'probability')
variate	('discrete', 'represented', 'quartile', 'quartile', 'measured', 'deviate', 'take', 'markov', 'covariance', 'sample', 'covariance', 'covariance', 'denoted', 'continuous', 'assumption', 'value', 'distribution', 'univariate', 'themselves', 'need', 'univariate', 'polynomial', 'reorder', 'statistically', 'probability', 'value', 'random', 'set', 'capital', 'probability', 'assumes', 'finite', 'need', 'matrix', 'random', 'multivariate', 'occur', 'distributed', 'distributed', 'distributed', 'random', 'state', 'space', 'random', 'variable', 'random', 'uniformly', 'nonuniformly', 'frequently', 'random', 'random', 'variable', 'statistic', 'uniform', 'continuous', 'generalization', 'practice', 'capital', 'probability', 'assumes', 'denoted', 'random', 'matrix', 'random', 'variable', 'absolutely', 'correlation', 'uniform', 'range', 'range', 'equal', 'taken', 'probability', 'value', 'distributed', 'distributed', 'beta', 'normal', 'cauchy', 'normal', 'continuous', 'normal', 'distribution', 'binomial', 'distributed', 'ratio', 'ratio', 'beta', 'gamma', 'gamma', 'distribution', 'parameter', 'beta', 'normal', 'gamma', 'parameter', 'normal', 'gaussian', 'identical', 'approximately', 'distribution', 'probability', 'normal', 'assumes', 'probability', 'value', 'unknown', 'distribution', 'two', 'variance', 'normal', 'uniform', 'probability', 'assumes', 'normal', 'assumes', 'normal', 'zero', 'zero', 'alternate', 'normal', 'form', 'interval', 'interval', 'interval', 'interval', 'greater', 'less', 'number', 'probability', 'value', 'function', 'set', 'standard', 'value', 'form', 'limiting', 'performed', 'normally', 'normal', 'suppose', 'bernoulli', 'satisfy', 'need')
represented	('variate', 'graphically', 'value', 'form')
graphically	('represented', 'plotting')
plotting	('graphically', 'know', 'distribution', 'positions', 'position', '#', 'distribution', 'rank', 'position', 'say', 'data', 'method', 'interval', 'number', 'chart', 'numeric', 'statistical', 'position', 'point', 'against')
drawing	('point', 'set', 'code', 'dot')
straight	('set', 'line', 'curve', 'diagonal', 'line', 'line', 'generalizing', 'line', 'necessarily')
line	('straight', 'segments', 'parallel', 'equality', 'parallel', 'equality', 'diagonal', 'inequality', 'below', 'enclosed', 'equality', 'under', 'computing', 'best', 'floor', 'defining', 'variable', 'shown', 'single', 'shown', 'shown', 'floor', 'distance', 'probability', 'fall', 'probability', 'one', 'slightly', 'nearest', 'angle', 'intersection', 'number', 'number', 'crossing', 'shown', 'several', 'buffon-laplace', 'shown', 'expressed', 'accompanied', 'concentration', 'disappears', 'probability', 'wiener', 'median', 'joining', 'trapezoid', 'segment', 'solving', 'multiple', 'regression', 'kenney', 'curved', 'kenney', 'offsets', 'best-fit', 'straight', 'through', 'data', 'straight', 'say', 'deviation', 'measured', 'procedure', 'best-fit', 'error', 'offset', 'best-fit', 'set', 'distance', 'point', 'straight', 'first', 'through', 'slope', 'using', 'horizontal', 'joined', 'data', 'graph', 'roughly', 'distance', 'fixed', 'real', 'mapped', 'image', 'segment')
segments	('line', 'connecting')
connecting	('segments', 'adjacent', 'equation', 'gumbel', 'formula', 'variable')
preferable	('point', 'use')
use	('preferable', 'summarized', 'many', 'error', 'kenney', 'notation', 'uninformative', 'check', 'additional', 'motivates', 'symbol', 'physical', 'term', 'following', 'somewhat', 'term', 'physical', 'term', 'quantity', 'uninformative', 'appropriate', 'common', 'term', 'involves', 'function', 'p', 'unfortunate', 'authors', 'alternative', 'addition', 'frequency', 'handled', 'ito', 'orientation', 'making', 'statistical', 'integral', 'bevington', 'still', 'linear', 'minimize', 'absolute', 'matrix', 'elementary', 'because', 'test', 'testing', 'authors', 'term', 'proper', 'vital', 'beyer', 'seggern', 'slightly', 'uniformly', 'term', 'symbol', 'distribution', 'box-muller', 'p', 'been', 'characteristic', 'large', 'stirling', 'completely')
grouped	('histogram', 'been', 'four', 'table', 'cumulant', 'distribution')
curve	('frequency', 'frequency', 'width', 'point', 'function', 'measure', 'lorenz', 'lorenz', 'lorenz', 'point', 'parallel', 'parallel', 'lorenz', 'lorenz', 'economics', 'lorenz', 'function', 'lorenz', 'polygon', 'lorenz', 'expressed', 'lorenz', 'straight', 'lorenz', 'total', 'lorenz', 'descriptive', 'moderate', 'moderate', 'moderate', 'above', 'function', 'red', 'right', 'top', 'right', 'best-fitting', 'set', 'sum', 'short-dashed', 'fit', 'long-dashed', 'fit', 'solid', 'initial', 'intermediate', 'solid', 'fit', 'fitting', 'necessarily', 'best-fit', 'arbitrary', 'including', 'smooth', 'limiting', 'frequency', 'statistical', 'frequency', 'frequency', 'one', 'kenney', 'normal', 'pearson', 'possesses')
ogive	('histogram', 'cumulative', 'polygon', 'relative', 'polygon', 'pie', 'figure', 'statistical')
full	('width', 'numerical', 'widths', 'welch', 'width', 'median', 'width')
width	('full', 'half', 'parameter', 'curve', 'full', 'half', 'height', 'function', 'half', 'half', 'full', 'sum')
half	('width', 'maximum', 'reaches', 'maximum', 'width', 'maximum', 'first', 'cell', 'written', 'width', 'width', 'maximum', 'distribution', 'normal', 'distribution', 'normal', 'excess', 'normal', 'function', 'normal', 'nails', 'lower', 'divided')
fwhm	('parameter',)
distance	('function', 'based', 'dissimilarity', 'line', 'shorter', 'two', 'longer', 'two', 'function', 'needle', 'rate', 'identity', 'traveled', 'traveling', 'absolute', 'root-mean-square', 'unit', 'travel', 'might', 'perpendicular', 'line', 'minimized', 'line', 'mahalanobis', 'two', 'within', 'mean', 'smaller')
reaches	('function', 'half', 'distribution', 'maximum')
analytic	('table', 'numerical', 'simpler', 'form', 'simpler', 'form', 'amenable', 'function', 'form')
widths	('full', 'several')
welch	('full',)
apodization	('statistics', 'function')
single	('distribution', 'distribution', 'mode', 'value', 'unique', 'possessing', 'unique', 'distribution', 'local', 'denoted', 'discrete', 'function', 'continuous', 'generate', 'cluster', 'symmetry', 'rectangle', 'intersecting', 'line', 'entirely', 'tile', 'betting', 'tile', 'entirely', 'tile', 'betting', 'tile', 'entirely', 'tile', 'betting', 'tile', 'lie', 'tile', 'betting', 'tile', 'roll', 'loaded', 'consisting', 'double', 'double', 'digit', 'start', 'digit', 'first', 'assign', 'number', 'no', 'test', 'trial', 'performance', 'fall', 'bin', 'distribution', 'unimodal')
gauss	('mode', 'inequality', 'who', 'early', 'two', 'derived', 'error', 'analysis')
inequality	('gauss', 'descriptive', 'measure', 'ecology', 'wealth', 'line', 'amount', 'summarized', 'estimator', 'robbin', 'boole', 'denotes', 'boole', 'probability', 'markov', 'probability', 'probability', 'statistical', 'probability', 'probability', 'cam', 'limit', 'khinchin', 'chebyshev', 'frivolous')
gini	('coefficient', 'coefficient', 'population', 'coefficient', 'et', 'coefficient', 'sample', 'coefficient', 'coefficient', 'statistic', 'coefficient', 'summarized', 'coefficient', 'ratio', 'statistic', 'coefficient')
statistic	('summary', 'lorenz', 'hinge', 'local', 'set', 'h', 'order', 'quartile', 'box', 'summary', 'lorenz', 'sample', 'ordered', 'gini', 'gini', 'mean', 'sample', 'maximum', 'order', 'mean', 'order', 'pearson', 'bimodal', 'percentile', 'percentile', 'percentile', 'finite', 'sample', 'floor', 'order', 'order', 'percentile', 'percentile', 'hinge', 'interquartile', 'interquartile', 'high', 'reversion', 'absolute', 'absolute', 'mean', 'high', 'absolute', 'absolute', 'unbiased', 'estimating', 'mean', 'order', 'pearson', 'order', 'range', 'midrange', 'fence', 'head', 'bimodal', 'u', 'descriptive', 'bimodal', 'harmonic', 'care', 'h', 'k', 'skewness', 'unbiased', 'parameter', 'central', 'generalize', 'symmetric', 'generalize', 'gamma', 'central', 'type', 'useful', 'order', 'descriptive', 'frequently', 'essentially', 'using', 'standard', 'gamma', 'graph', 'through', 'mean', 'bivariate', 'cluster', 'cluster', 'bivariate', 'univariate', 'bivariate', 'almost', 'using', 'order', 'hogg', 'order', 'rank', 'extreme', 'nonparametric', 'sample', 'rank', 'proposed', 'correlation', 'p-value', 'appropriate', 'test', 'total', 'critical', 'completely', 'probability', 'several', 'likelihood', 'uniform', 'asymptotic', 'probability', 'data', 'random', 'darling', 'kuiper', 'kuiper', 'variate', 'law', 'random', 'value', 'median', 'rank', 'hinge', 'trimean', 'symmetric', 'inversion', 'upper', 'degenhardt', 'inversion', 'rank', 'inversion', 'inversion', 'symmetric', 'order', 'relatively', 'improve', 'darling', 'kuiper', 'pearson', 'most', 'hypothesis', 'probability', 'assess', 'test', 'least', 'test', 'type', 'darling', 'd', 'd', 'kuiper', 'kuiper', 'normal', 'improve', 'kuiper', 'darling', 'test', 'multivariate', 'test', 'negative', 'predictive', 'sensitivity', 'specificity', 'true', 'test', 'negative', 'always', 'uncorrelated', 'markov', 'sampling', 'trial', 'distribution', 'order', 'weibull', 'freedom', 'ratio', 'distribution', 'domain', 'distribution', 'variance', 'distribution', 'certain', 'uniform', 'most')
lorenz	('statistic', 'statistics', 'asymmetry', 'coefficient', 'curve', 'asymmetry', 'statistic', 'curve', 'asymmetry', 'curve', 'asymmetry', 'function', 'point', 'point', 'less', 'asymmetry', 'coefficient', 'curve', 'curve', 'size', 'curve', 'sample', 'curve', 'alternatively', 'curve', 'size', 'curve', 'size', 'curve', 'equality', 'measured', 'asymmetry', 'coefficient', 'curve', 'coefficient', 'asymmetry')
unordered	('easily', 'size')
mean	('data', 'data', 'difference', 'divided', 'size', 'absolute', 'statistic', 'deviation', 'maximum', 'minimum', 'statistical', 'statistic', 'order', 'plot', 'regression', 'descriptive', 'reversion', 'regression', 'statistical', 'greater', 'proportion', 'closer', 'you', 'reversion', 'reversion', 'descriptive', 'statistic', 'shown', 'deviation', 'deviation', 'order', 'population', 'most', 'variance', 'variance', 'less', 'large', 'statistic', 'midrange', 'confidence', 'deviation', 'within', 'centered', 'normal', 'difference', 'deviation', 'sample', 'estimator', 'population', 'square', 'sample', 'sample', 'variable', 'likelihood', 'moment', 'sample', 'population', 'kurtosis', 'moment', 'poisson', 'first', 'sample', 'sample', 'sample', 'set', 'notation', 'sample', 'list', 'statistical', 'sample', 'arithmetic', 'arithmetic', 'population', 'population', 'sample', 'sample', 'sample', 'estimated', 'sample', 'sample', 'deviation', 'deviation', 'zero', 'above', 'denotes', 'written', 'kurtosis', 'moment', 'excess', 'skewness', 'harmonic', 'geometric', 'arithmetic-geometric', 'satisfy', 'again', 'geometric', 'arithmetic-geometric', 'arithmetic', 'quantity', 'set', 'notation', 'set', 'notation', 'list', 'general', 'homogeneous', 'property', 'set', 'joke', 'told', 'runs', 'fact', 'two', 'duck', 'arithmetic', 'arithmetic', 'geometric', 'central', 'geometric', 'harmonic', 'harmonic', 'lehmer', 'lehmer', 'lehmer', 'deviation', 'power', 'reversion', 'reversion', 'root', 'root', 'square', 'sample', 'standard', 'stolarsky', 'deviation', 'deviation', 'absolute', 'absolute', 'sample', 'size', 'deviation', 'distribution', 'deviation', 'data', 'deviation', 'distribution', 'deviation', 'because', 'deviation', 'hand', 'deviation', 'summarizes', 'absolute', 'summarizes', 'absolute', 'distribution', 'deviation', 'square', 'msd', 'square', 'denoted', 'central', 'equal', 'kurtosis', 'moment', 'walk', 'square', 'skewness', 'mode', 'statistical', 'distribution', 'population', 'expectation', 'population', 'distribution', 'unbiased', 'population', 'population', 'arithmetic', 'arithmetic', 'population', 'sample', 'using', 'moment', 'moment', 'deviation', 'deviation', 'root', 'square', 'square', 'root', 'denotes', 'hoehn', 'root', 'squared', 'root', 'square', 'geometric', 'arithmetic', 'harmonic', 'geometric', 'geometric', 'harmonic', 'harmonic', 'harmonic', 'geometric', 'geometric', 'geometric', 'square', 'power', 'pythagorean', 'standard', 'sample', 'computed', 'need', 'true', 'expected', 'depend', 'underlying', 'moment', 'distribution', 'kurtosis', 'momental', 'second', 'square', 'root', 'squared', 'descriptive', 'statistic', 'interval', 'interval', 'deviation', 'root', 'square', 'violet', 'kenney', 'based', 'press', 'population', 'probable', 'sample', 'standard', 'population', 'denotes', 'sample', 'estimated', 'propagation', 'moment', 'variation', 'moment', 'standard', 'adjective', 'involving', 'distribution', 'vector', 'distribution', 'vector', 'theory', 'word', 'chance', 'gaps', 'net', 'two', 'conditional', 'uniform', 'parzen', 'random', 'generating', 'number', 'right', 'number', 'conjectured', 'square', 'gaussian', 'variance', 'estimate', 'statistical', 'quantities', 'block', 'next', 'number', 'value', 'cluster', 'site', 'cluster', 'satisfies', 'run', 'site', 'run', 'distributed', 'variance', 'geometric', 'index', 'harmonic', 'index', 'geometric', 'harmonic', 'geometric', 'index', 'harmonic', 'index', 'two', 'arithmetic', 'two', 'arithmetic', 'correlation', 'correlation', 'difference', 'tukey', 'difference', 'analysis', 'square', 'level', 'level', 'entries', 'f-ratio', 'squared', 'ss', 'same', 'observed', 'variance', 'unknown', 'observed', 'observed', 'variance', 'unknown', 'two', 'two', 'equality', 'pair', 'differ', 'standard', 'subsequences', 'average', 'moving', 'arithmetic', 'correlation', 'sample', 'sample', 'sample', 'sample', 'sample', 'distribution', 'equal', 'standard', 'characteristic', 'standard', 'parameter', 'zero', 'unit', 'function', 'scaling', 'case', 'second', 'distribution', 'two', 'set', 'distributed', 'standard', 'distribution', 'variance', 'universe', 'within', 'distance', 'universe', 'unit', 'sample', 'probability', 'certain', 'population', 'raw', 'normalized', 'form', 'concentration', 'circular', 'estimator', 'bernoulli', 'sample', 'population', 'population', 'relation', 'independent', 'discrete', 'excess', 'relation', 'population', 'p', 'distribution', 'distribution', 'sample', 'function', 'distribution', 'function', 'above', 'term', 'number', 'satisfies', 'density', 'finite', 'lindeberg', 'standard', 'sample')
difference	('mean', 'possible', 'quartile', 'measured', 'number', 'quantity', 'deviation', 'mean', 'quantity', 'only', 'cluster-based', 'paired', 'count', 'coefficient', 'statistical', 'paired', 'rank', 'too', 'interval', 'event', 'one', 'distribution', 'expansion', 'distribution', 'one', 'big', 'zero', 'random', 'point', 'vertical', 'left', 'bland-altman', 'plot', 'value', 'thereof', 'coefficient', 'method', 'plot', 'mean', 'plot', 'mean', 'plot', 'chi-square', 'larger', 'proportion', 'independent', 'estimator', 'doing', 'spencer', 'covariance', 'table', 'distribution', 'successes', 'gaussian', 'distribution', 'normal', 'distribution', 'two', 'distribution', 'two', 'normal', 'distribution', 'normal', 'two', 'normal', 'distribution', 'normal', 'distribution', 'normal', 'distribution', 'probability', 'two', 'two', 'uniform', 'distribution', 'uniform', 'distribution', 'uniform', 'distribution', 'uniform', 'distribution', 'uniform', 'distribution', 'absolute', 'number', 'quantity', 'largest', 'distribution', 'distribution', 'percentage', 'expected')
individuals	('divided', 'dixon', 'zero')
divided	('individuals', 'mean', 'distribution', 'total', 'deviation', 'half', 'number')
dixon	('size', 'et', 'individuals', 'et', 'paper', 'et')
et	('dixon', 'damgaard', 'dixon', 'damgaard', 'dixon', 'gini', 'evans', 'particular', 'hoaglin', 'moore', 'press', 'empirical', 'kendall', 'sheppard', 'kendall', 'following', 'press', 'bacry', 'stands', 'carlsson', 'hawkes', 'altares', 'diaconis', 'proposed', 'diaconis', 'estimated', 'bartoš', 'who', 'bartoš', 'counterintuitive', 'berlekamp', 'evans', 'confuse', 'evans', 'probability', 'evans', 'cuyt', 'evans', 'specific', 'evans', 'blom', 'blom', 'evans', 'edelman', 'edelman', 'evans', 'specific', 'graham', 'plugging', 'mosteller', 'konig', 'press', 'tukey', 'jodár', 'matrix', 'press', 'gordon', 'schilling', 'ziff', 'cluster', 'evans', 'thompson', 'sampling', 'evans', 'johnson', 'evans', 'typo', 'evans', 'johnson', 'other', 'evans', 'evans', 'evans', 'evans', 'evans')
damgaard	('et', 'weiner', 'et', 'weiner')
weiner	('damgaard', 'damgaard', 'correcting')
alternatively	('data', 'lorenz')
ordered	('data', 'increasing', 'statistic', 'size', 'proportion', 'sample', 'function', 'set', 'element', 'particular', 'sequence', 'table', 'criterion', 'data', 'time')
increasing	('ordered', 'size', 'data', 'order', 'monotone', 'monotonic', 'surely', 'long')
correcting	('weiner', 'typographical', 'self', 'point', 'self', 'point', 'self', 'point', 'self', 'point', 'self', 'point', 'self', 'point', 'self', 'point', 'self', 'point', 'function', 'sign')
typographical	('correcting', 'error')
denominator	('error', 'original')
paper	('original', 'dixon', 'probability', 'quantile')
minimum	('range', 'value', 'mean', 'order', 'variance', 'compared', 'variance', 'compared', 'midrange', 'statistical', 'approximation', 'number', 'uniformly', 'variance', 'uniformly', 'variance', 'tosses', 'number', 'guesses', 'expensive', 'time', 'number', 'condition', 'linear', 'form', 'former', 'above', 'arbitrary', 'maximum', 'finding', 'distribution', 'extreme', 'distribution', 'gumbel')
zero	('individuals', 'been', 'distribution', 'kurtosis', 'television', 'equal', 'distribution', 'mean', 'using', 'one', 'distribution', 'th', 'equal', 'occurring', 'disk', 'thickness', 'random', 'abbreviation', 'value', 'row', 'difference', 'variance', 'argument', 'approach', 'faster', 'general', 'multivariate-distributed', 'mean', 'variate', 'variate', 'distribution', 'law', 'distribution', 'expectation')
theoretical	('equal', 'maximum', 'kurtosis', 'distribution')
infinite	('one', 'population', 'practically', 'top', 'one', 'peakedness', 'probability', 'number', 'problem', 'equally', 'countably', 'random', 'distribution', 'variance', 'variance', 'sample', 'normally', 'population')
individual	('population', 'except', 'size', 'mapped', 'size', 'size', 'sample', 'average', 'same', 'probabilities', 'pennies', 'several', 'maintaining', 'data', 'appropriate', 'false', 'test', 'appropriate', 'variance', 'term', 'guarantees')
except	('individual', 'one', 'q1', 'a006928', 'second', 'data')
shown	('been', 'sample', 'mean', 'equal', 'line', 'line', 'line', 'line', 'red', 'missing', 'line', 'figure', 'figure', 'figure', 'equal', 'figure', 'bet', 'point', 'net', 'two', 'example', 'above', 'easily', 'above', 'large', 'grünbaum', 'data', 'function', 'thin', 'verified', 'uspensky', 'probability', 'axis')
need	('above', 'multiplied', 'sample', 'unbiased', 'mean', 'value', 'stored', 'sample', 'unbiased', 'variate', 'variate', 'edge', 'distribution', 'normal', 'lowered', 'lowered', 'variate', 'necessarily')
multiplied	('need', 'order', 'row', 'additional')
become	('order', 'unbiased', 'large', 'oeis', 'oeis', 'oeis', 'generalized', 'truly', 'order', 'plugging', 'element', 'smaller', 'very', 'usual', 'singly', 'normal', 'sample', 'size', 'geometric')
unbiased	('become', 'q8', 'approximate', 'estimate', 'approximately', 'estimate', 'other', 'statistic', 'estimator', 'estimator', 'variance', 'estimator', 'estimator', 'estimator', 'estimator', 'estimator', 'symmetric', 'other', 'symmetric', 'other', 'first', 'population', 'size', 'statistic', 'estimator', 'distribution', 'need', 'variance', 'notation', 'sample', 'general', 'even', 'deviation', 'estimator', 'estimator', 'estimator', 'estimator', 'estimator', 'k', 'skewness', 'estimator', 'mean', 'moment', 'variance', 'above', 'obtain', 'estimator', 'need', 'variance', 'estimator', 'variance', 'estimator', 'asymptotically', 'estimator', 'observed', 'independent', 'formalism', 'indeed')
asymmetry	('lorenz', 'coefficient', 'lorenz', 'coefficient', 'degree', 'lorenz', 'lorenz', 'coefficient', 'lorenz', 'coefficient', 'degree', 'around', 'lorenz', 'lorenz', 'coefficient', 'moderate', 'kenney', 'moderate', 'kenney', 'moderate', 'kenney', 'determining', 'tailedness', 'degree')
same	('hinges', 'interquartile', 'individual', 'sample', 'size', 'essentially', 'q1', 'distribution', 'group', 'solving', 'constructed', 'duals', 'trial', 'probability', 'viswanath', 'constant', 'produce', 'output', 'visits', 'lattice', 'step', 'number', 'land', 'lattice', 'typically', 'performing', 'operations', 'performing', 'operations', 'a000002', 'oeis', 'card', 'color', 'card', 'normal', 'clumps', 'value', 'dot', 'quantile-quantile', 'restricting', 'factor', 'mean', 'different', 'restricted', 'factor', 'sample', 'variable', 'normal', 'distribution', 'element', 'function', 'functional', 'surrogates', 'probability', 'necessarily')
h	('point', 'spread', 'statistic', 'spread', 'plot', 'spread', 'fence', 'spread', 'mathstatica', 'statistic', 'originally', 'up', 's')
spread	('h', 'descriptive', 'h', 'haberdasher', 'h', 'hinge', 'h', 'model')
hinge	('statistic', 'interquartile', 'descriptive', 'ordering', 'central', 'identical', 'h-spread', 'descriptive', 'problem', 'theorem', 'spread', 'quartile', 'identical', 'statistic', 'interquartile', 'distribution', 'maximum', 'statistical', 'statistic', 'l', 'tukey', 'plot', 'histogram', 'statistical')
high-water	('value', 'maxima', 'number', 'maximum')
sequence	('example', 'running', 'maxima', 'example', 'running', 'above', 'occur', 'unimodal', 'independent', 'random', 'value', 'markov', 'markov', 'monte', 'random', 'markov', 'satisfy', 'markov', 'markov', 'moment', 'skewness', 'follow', 'interval', 'moment', 'hausdorff', 'conditions', 'moment', 'moment', 'moment', 'moment', 'moment', 'function', 'moment', 'moment', 'moment', 'record', 'ht', 'oeis', 'random', 'spp', 'time', 'strictly', 'spp', 'random', 'quasirandom', 'uniform', 'generate', 'random', 'random', 'net', 'context', 'alone', 'quasirandom', 'random', 'quasirandom', 'random', 'fills', 'ordinary', 'produce', 'big', 'outputs', 'point', 'extremely', 'quasirandom', 'stopping', 'quasirandom', 'random', 'corput', 'following', 'fibonacci', 'real', 'quasirandom', 'random', 'uniform', 'uniform', 'quasirandom', 'uniform', 'one-dimensional', 'generate', 'divide', 'van', 'constrained', 'corput', 'base', 'corput', 'random', 'quasirandom', 'random', 'walk', 'discrete', 'ordered', 'finch', 'number', 'self-describing', 'consisting', 'start', 'block', 'obtain', 'added', 'obtain', 'oeis', 'a006928', 'successive', 'length', 'a042942', 'started', 'identical', 'oeis', 'kolakoski', 'kolakoski', 'run', 'run', 'one', 'case', 'fibonacci', 'recurrence', 'negative', 'yield', 'oeis', 'split', 'maximal', 'length', 'falling', 'say', 'run', 'average', 'new', 'arithmetic', 'uncorrelated', 'stage', 'form', 'wiener', 'equidistributed', 'random', 'independent', 'independent', 'hold', 'lindeberg', 'convergence', 'kolmogorov', 'number', 'mutually', 'theorem', 'independent')
measurements	('mark', 'seen', 'orderings', 'third', 'trials', 'plotted', 'records', 'oeis', 'number', 'obtain')
seen	('measurements', 'noting', 'toss', 'probability', 'subject', 'point', 'exist', 'premultiplying', 'distribution', 'characteristic', 'distribution', 'parameter', 'cumulant-generating')
measurement	('first', 'definition', 'second', 'equally', 'outliers', 'interval', 'trial', 'probability', 'normal', 'contained', 'frequently', 'contained', 'treatise', 'compass', 'type', 'probability', 'monthly', 'processing', 'signal', 'study', 'population')
record	('definition', 'contributes', 'third', 'contributes', 'setting', 'over', 'sequence')
contributes	('record', 'second', 'first', 'two', 'record', 'havil')
equally	('measurement', 'likely', 'room', 'large', 'value', 'out', 'possible', 'grid', 'spaced', 'floor', 'spaced', 'infinite', 'spaced', 'occur', 'likely', 'step', 'likely', 'area', 'step', 'likely', 'distribution', 'likely', 'better', 'likely')
likely	('equally', 'higher', 'event', 'followed', 'observation', 'reason', 'slightly', 'land', 'twice', 'triple', 'time', 'time', 'least', 'newton', 'asymptotically', 'equally', 'keynes', 'most', 'goldstein', 'equally', 'either', 'equally', 'equally', 'quite', 'least', 'distribution', 'equally', 'thing', 'happen')
higher	('likely', 'lower', 'access', 'word', 'peak', 'slightly', 'probability', 'suspected', 'mathematical', 'variance', 'constant', 'order', 'term', 'probability')
lower	('higher', 'first', 'upper', 'upper', 'order', 'half', 'ball')
orderings	('possible', 'measurements')
third	('measurements', 'record', 'first', 'interquartile', 'above', 'first', 'first', 'first', 'interquartile', 'first', 'interquartile', 'equal', 'standardized', 'considering', 'term', '◇', 'term', 'distribution', 'ane', 'fourth', 'anomalous', 'different', 'person', 'up', 'ex', 'watson', 'block')
havil	('contributes', 'tosses', 'constant', 'data')
pp	('comparison', 'continuous', 'kenney', 'transitional', 'kurtosis', 'function', 'romanovsky', 'whittaker', 'robust', 'bayes', 'derivation', 'laplace', 'probabilities', 'uspensky', 'reproduced', 'size', 'experiments', 'vere-jones', 'notion', 'principle', 'principle', 'viswanath', 'pugh', 'correlation', 'gonick', 'standard', 'oeis', 'bernoulli', 'kenney', 'de', 'probability', 'fitting', 'chi', 'outcome', 'raw', 'demonstrated', 'considers', 'prefer', 'pfeiffer', 'cumulant-generating', 'weak')
comparison	('pp', 'number', 'population', 'probability', 'set', 'order', 'equal', 'value', 'equal', 'first', 'critical', 'population', 'statistical', 'set', 'order', 'statistical')
records	('number', 'set', 'number', 'measurements', 'obtain', 'a004080', 'oeis')
trials	('random', 'measurements')
plotted	('measurements', 'function', 'above', 'complex', 'above', 'distribution', 'above', 'g-function', 'above', 'distribution', 'above')
oeis	('measurements', 'value', 'records', 'romanovsky', 'obtain', 'birthdays', 'formula', 'mosteller', 'become', 'become', 'become', 'term', 'sequence', 'value', 'value', 'value', 'one', 'column', 'zucker', 'a086230', 'value', 'step', 'step', 'value', 'length', 'paths', 'paths', 'sequence', 'step', 'sequence', 'same', 'step', 'less', 'fraction', 'number', 'pp', 'polynomial', 'sequence', 'multiplying', 'small', 'number', 'numerically', 'first', 'erf', 'erf', 'maximum', 'point', 'a133839', 'value', 'distribution', 'value', 'term', 'integer', 'value', 'value', 'number', 'function', 'large', 'integrand', 'mannion')
a055980	('number',)
a004080	('records',)
a096618	('high',)
water	('high', 'mark', 'high', 'mark', 'high', 'high', 'mark')
ordering	('hinge', 'data')
writing	('order', 'out', 'integral', 'expanding', 'kunkel', 'plot', 'analytically', 'plugging', 'analytically', 'plugging', 'fit', 'premultiplying', 'simultaneously', 'general')
shape	('out', 'extended', 'convex', 'formed', 'wires', 'mouth', 'social', 'platykurtic')
bottom	('value', 'legs', 'firing', 'randomize', 'even', 'trial', 'crosses', 'row')
legs	('bottom',)
peak	('central', 'statistical', 'sharper', 'higher', 'high', 'kurtosis')
identical	('hinge', 'hinge', 'first', 'variable', 'immediately', 'two', 'tosses', 'variable', 'virtually', 'sequence', 'consecutive', 'a-series', 'formal', 'set', 'set', 'set', 'under', 'coefficient', 'variate', 'exponential', 'surrogates', 'power')
h-spread	('hinge', 'step')
haberdasher	('spread', 'problem')
theorem	('hinge', 'order', 'minimax', 'doob', 'process', 'markov', 'horn', 'majorization', 'esseen', 'limit', 'price', 'trivariate', 'variable', 'normal', 'bayes', 'probability', 'probability', 'beautiful', 'exact', 'bayes', 'fermat', 'probability', 'bayes', 'conditional', 'complement', 'uncorrelated', 'probability', 'bayes', 'conditional', 'probability', 'probability', 'bayes', 'conditional', 'discrepancy', 'discrete', 'due', 'hudson-parthasarathy', 'first', 'second', 'moivre-laplace', 'fact', 'laplace', 'statistical', 'poisson', 'estimate', 'poisson', 'statistical', 'sampling', 'shah', 'sklar', 'doob', 'doob', 'continuous', 'asymptotic', 'multivariate', 'variable', 'continuous', 'limit', 'limit', 'erf', 'esseen', 'confidence', 'normal', 'cramer', 'normal', 'price', 'continuous', 'laplace', 'galton', 'cochran', 'cochran', 'discrete', 'poisson', 'sklar', 'general', 'inverse', 'limit', 'data', 'limit', 'limit', 'berry', 'esseen', 'fourier', 'limit', 'lyapunov', 'cramer', 'limit', 'normal', 'berry', 'esseen', 'central', 'limit', 'lindeberg', 'converse', 'cochran', 'fisher', 'fisher', 'limit', 'chi', 'cochran', 'correlation', 'expressing', 'strong', 'coincidence', 'frivolous', 'arithmetic', 'bernoulli', 'random', 'central', 'limit', 'feller', 'limit', 'limit', 'berry', 'esseen', 'central', 'limit', 'feller', 'th', 'central', 'limit', 'frivolous', 'frivolous', 'arithmetic', 'sequence', 'asymptotic', 'limit', 'chebyshev', 'frivolous', 'arithmetic')
median	('statistical', 'trimean', 'plus', 'low', 'statistical', 'statistical', 'mode', 'statistical', 'plot', 'statistical', 'statistical', 'random', 'denoted', 'list', 'measured', 'p', 'less', 'population', 'population', 'mode', 'statistical', 'rank', 'statistical', 'statistical', 'variance', 'hogg', 'statistical', 'quartile', 'order', 'statistical', 'intersect', 'centroid', 'line', 'face', 'side', 'rank', 'statistic', 'triangle', 'statistical', 'tetrahedron', 'tetrahedron', 'trapezoid', 'triangle', 'press', 'statistical', 'horizontal', 'statistical', 'upper', 'moving', 'spencer', 'cauchy', 'full')
trimean	('median', 'l', 'stolarsky', 'variance', 'l-estimate', 'rank', 'tukey', 'rank', 'statistic')
divide	('set', 'point', 'sample', 'point', 'sample', 'vertices', 'sample', 'range', 'coefficient', 'fisher', 'sequence', 'interval', 'one', 'volume')
low	('equal', 'median', 'high', 'two', 'two', 'high')
even	('number', 'calculation', 'including', 'deviation', 'unbiased', 'case', 'odd', 'perhaps', 'true', 'two', 'matter', 'term', 'bankrupt', 'equal', 'permutation', 'either', 'set', 'sum', 'bottom', 'value', 'sample', 'exponent', 'combining', 'matrix', 'necessarily', 'possible', 'oscillation', 'none', 'number', 'fixed', 'complete', 'tossed', 'number', 'p')
consisting	('group', 'distribution', 'possible', 'event', 'occurrence', 'grid', 'equilateral', 'sequence', 'single', 'object', 'following', 'field', 'certain', 'trial', 'distribution', 'sum')
either	('point', 'side', 'rank', 'up', 'programmer', 'create', 'system', 'form', 'rest', 'side', 'occur', 'pennies', 'player', 'space', 'finite', 'interpreted', 'time', 'even', 'odd', 'likely', 'example', 'constant', 'perfectly', 'test', 'pearson', 'say', 'mathematics', 'extractions', 'computed', 'extractions', 'computed')
side	('either', 'statistical', 'right', 'differentiate', 'wherever', 'series', 'needle', 'rhombi', 'length', 'shortening', 'square', 'square', 'length', 'shortening', 'equilateral', 'triangle', 'length', 'shortening', 'regular', 'triangle', 'length', 'rhombus', 'length', 'either', 'face', 'top', 'facing', 'land', 'initially', 'initial', 'facing', 'heavy', 'close', 'median', 'best-fit', 'create', 'defining', 'draw', 'draw', 'gonick', 'mercator')
plus	('median', 'statistical', 'word', 'overflow', 'error', 'minus', 'appear', 'original')
odd	('number', 'even', 'containing', 'integral', 'principle', 'longer', 'skewed', 'written', 'winning', 'probability', 'either', 'goldstine', 'sum', 'large', 'value', 'sample', 'integral', 'number', 'case', 'th')
find	('point', 'statistical', 'conversely', 'only', 'algebra', 'ci', 'standard', 'analysis', 'asks', 'probability', 'asks', 'probability', 'try', 'earliest', 'case', 'probability', 'variable', 'mistakes', 'list', 'statistical', 'minimized', 'best', 'function', 'possible', 'distribution', 'greatest', 'explicitly', 'integral', 'central', 'excess', 'approximation', 'set', 'solve')
denoting	('group', 'first', 'consistent')
box	('statistic', 'whisker', 'distribution', 'muller', 'probability', 'whisker', 'yield', 'muller', 'shuffle', 'muller', 'plot', 'draw', 'extend', 'draw', 'fence', 'whisker', 'chart', 'whisker', 'distribution', 'muller')
whisker	('box', 'plot', 'box', 'plot', 'extreme', 'only', 'box', 'plot', 'box', 'plot')
plot	('whisker', 'h', 'histogram', 'compares', 'quantile', 'quartile', 'mean', 'median', 'normal', 'quantile', 'quartile', 'writing', 'above', 'whisker', 'buffon', 'predictor', 'run', 'above', 'small', 'right', 'three', 'emphasized', 'degree', 'recurrence', 'statistical', 'solving', 'short-dashed', 'predictor', 'kolakoski', 'above', 'fraction', 'graph', 'set', 'dot', 'dot', 'histogram', 'pareto', 'pie', 'bland-altman', 'data', 'difference', 'mean-difference', 'tukey', 'specific', 'tendency', 'common', 'set', 'arithmetic', 'altman', 'statistical', 'arithmetic', 'box-and-whisker', 'box', 'draw', 'wolfram', 'whisker', 'statistical', 'dot', 'dot', 'hinge', 'cumulative', 'absolute', 'difference', 'statistical', 'bland', 'altman', 'dot', 'count', 'above', 'random', 'dot', 'wolfram', 'dot', 'statistical', 'bar', 'whisker', 'histogram', 'frequency', 'bar', 'dot', 'frequency', 'difference', 'statistical', 'bland', 'altman', 'frequency', 'pareto', 'type', 'type', 'quality', 'pareto', 'statistical', 'bar', 'arc', 'q', 'statistical', 'quantile', 'quantile', 'quantile', 'q-q', 'two', 'quantile', 'statistical', 'diagram', 'two', 'splitting', 'histogram', 'stem', 'difference', 'statistical', 'bland', 'altman', 'predictor', 'statistical', 'average', 'above', 'various', 'below', 'above', 'distribution')
degree	('measure', 'asymmetry', 'equality', 'asymmetry', 'quantity', 'distribution', 'peakedness', 'measure', 'asymmetry', 'freedom', 'small', 'wobble', 'polynomial', 'correlation', 'two', 'plot', 'correlation', 'first', 'th', 'polynomial', 'freedom', 'freedom', 'freedom', 'freedom', 'freedom', 'freedom', 'freedom', 'freedom', 'freedom')
parallel	('curve', 'line', 'curve', 'line', 'spaced')
equality	('line', 'above', 'line', 'below', 'total', 'line', 'lorenz', 'degree', 'beautiful', 'test', 'testing', 'mean', 'test')
axis	('above', 'below', 'around', 'symmetry', 'vertical', 'shown')
correspondingly	('point',)
symmetry	('sample', 'axis', 'measured', 'single', 'number')
equations	('following', 'number')
economics	('curve', 'ecology', 'aspects', 'stable')
ecology	('economics', 'inequality')
wealth	('inequality',)
proportion	('cumulative', 'ordered', 'cumulative', 'cumulative', 'data', 'mean', 'distribution', 'what', 'word', 'accounted', 'coefficient', 'accounted', 'difference', 'no', 'sample', 'sample', 'sample', 'fraction', 'sample', 'bayesian', 'standard', 'sample', 'success')
mapped	('individual', 'onto', 'line', 'onto')
onto	('mapped', 'cumulative', 'mapped', 'half-infinite', 'vertically', 'uppermost')
joining	('polygon', 'line', 'vertex')
expressed	('curve', 'cumulative', 'number', 'scientific', 'moment', 'moment', 'moment', 'moment', 'cumulant', 'moment', 'moment', 'moment', 'equation', 'using', 'occur', 'linear', 'certainty', 'line', 'erf', 'erf', 'distribution')
diagonal	('straight', 'line')
amount	('total', 'inequality', 'extremely', 'significant', 'additional', 'fixed', 'finite', 'money', 'hole', 'money', 'distinction', 'final', 'net', 'won', 'account', 'lost', 'large', 'player', 'wedges', 'effect', 'chance')
summarized	('inequality', 'gini', 'use', 'following', 'formula', 'following', 'solids', 'table', 'size', 'following', 'curtailed', 'following', 'results', 'following')
area	('ratio', 'enclosed', 'triangular', 'under', 'shaded', 'above', 'differential', 'equally', 'science')
enclosed	('area', 'line')
triangular	('total', 'area', 's', 'distribution', 'triangle', 'probabilities', 'tile', 'figure', 'tittman', 'lattice', 'upper', 'apex', 'lattice', 'distribution', 'symmetric', 'distribution', 'b', 'distribution', 'excess', 'distribution', 'function', 'distribution', 'leading', 'array')
around	('asymmetry', 'axis', 'placed', 'occur', 'time')
measured	('symmetry', 'lorenz', 'next', 'variate', 'median', 'ratio', 'difference', 'inferred', 'estimated', 'quantity', 'inferred', 'distribution', 'distribution', 'applied', 'variability', 'line', 'perpendicular', 'other', 'greater', 'value', 'set')
deviation	('absolute', 'descriptive', 'mean', 'quartile', 'quartile', 'quartile', 'descriptive', 'quartile', 'greater', 'random', 'signed', 'average', 'average', 'signed', 'signed', 'descriptive', 'absolute', 'absolute', 'mean', 'mean', 'quartile', 'quartile', 'standard', 'standard', 'statistical', 'absolute', 'signed', 'signed', 'variance', 'kenney', 'mean', 'standard', 'one', 'error', 'absolute', 'average', 'absolute', 'difference', 'mean', 'signed', 'signed', 'standard', 'standard', 'statistical', 'sample', 'standard', 'sample', 'biased', 'weighted', 'even', 'standard', 'unbiased', 'absolute', 'absolute', 'absolute', 'moment', 'mean', 'mean', 'relative', 'relative', 'signed', 'signed', 'standard', 'standard', 'absolute', 'absolute', 'absolute', 'relative', 'relative', 'standard', 'standard', 'variance', 'derived', 'gamma', 'standard', 'mean', 'pearson', 'standard', 'stolarsky', 'mean', 'mean', 'set', 'mean', 'mean', 'list', 'mean', 'discrete', 'mean', 'important', 'mean', 'natural', 'definition', 'introduction', 'least', 'straightforward', 'mean', 'closed', 'named', 'named', 'mean', 'absolute', 'standard', 'standard', 'variance', 'characteristic', 'standard', 'standardized', 'pearson', 'pearson', 'relative', 'relative', 'relative', 'absolute', 'absolute', 'mean', 'mean', 'signed', 'signed', 'standard', 'standard', 'square', 'squared', 'signal', 'standard', 'statistical', 'standard', 'distribution', 'standard', 'standard', 'probability', 'standard', 'sample', 'standard', 'standard', 'standard', 'list', 'standard', 'square', 'squared', 'quantity', 'standard', 'naturally', 'average', 'standard', 'standard', 'distribution', 'standard', 'again', 'standard', 'range', 'standard', 'mean', 'moment', 'standard', 'distribution', 'standard', 'distribution', 'standard', 'divided', 'sample', 'standard', 'variance', 'reason', 'set', 'standard', ';', 'measure', 'point', 'root-mean-square', 'distribution', 'data', 'set', 'line', 'point', 'maximum', 'true', 'best-fit', 'measure', 'sample', 'greater', 'independence', 'relaxation', 'standard', 'probability', 'true', 'sample', 'bernoulli', 'special', 'uniform', 'geometric', 'poisson', 'hurwitz', 'new')
kurtosis	('zero', 'moments', 'leptokurtic', 'population', 'sample', 'cumulant', 'mean', 'cumulant', 'moment', 'transform', 'mean', 'graph', 'moore', 'moment', 'skewness', 'moment', 'raw', 'normalized', 'most', 'termed', 'denoted', 'pp', 'theoretical', 'dist', 'p', 'equal', 'proper', 'reason', 'correspondence', 'peakedness', 'one', 'negative', 'excess', 'westfall', 'excess', 'excess', 'peak', 'moment', 'mesokurtic', 'moment', 'mean', 'skewness', 'skewness', 'mean', 'moment', 'moment', 'variance', 'skewness', 'skewness', 'skewness', 'skewness', 'skewness', 'skewness', 'skewness', 'skewness', 'skewness', 'skewness', 'skewness', 'skewness', 'skewness', 'skewness', 'skewness', 'skewness', 'skewness', 'skewness', 'skewness', 'skewness', 'skewness', 'skewness', 'skewness', 'skewness', 'skewness', 'skewness', 'skewness', 'skewness', 'skewness', 'skewness', 'skewness', 'skewness', 'skewness', 'skewness', 'skewness', 'skewness', 'skewness', 'skewness', 'skewness', 'skewness', 'skewness', 'skewness', 'skewness', 'distribution', 'distribution', 'leptokurtic')
excess	('mesokurtic', 'church', 'k', 'distribution', 'distribution', 'theory', 'refers', 'number', 'moore', 'graph', 'kenney', 'because', 'historically', 'kurtosis', 'moment', 'kurtosis', 'kurtosis', 'mean', 'satisfies', 'distribution', 'higher-order', 'expectation', 'chi', 'distribution', 'characteristic', 'exponential', 'characteristic', 'probability', 'gamma', 'gibrat', 'euler-mascheroni', 'taken', 'half', 'inverse', 'laplace', 'direct', 'slightly', 'logistic', 'characteristic', 'raw', 'cumulant-generating', 'pareto', 'pearson', 'characteristic', 'characteristic', 'first', 'student', 'characteristic', 'triangular', 'uniform', 'gamma', 'find', 'first', 'mean', 'case', 'case', 'log', 'quantities', 'written', 'characteristic', 'flattened')
mesokurtic	('excess', 'moments', 'kurtosis', 'platykurtic', 'leptokurtic')
moments	('mesokurtic', 'kurtosis')
leptokurtic	('kurtosis', 'platykurtic', 'satisfies', 'kurtosis', 'mesokurtic')
platykurtic	('leptokurtic', 'mesokurtic', 'shape', 'general')
midrange	('size', 'random', 'p', 'rank', 'mean', 'mode', 'statistic', 'range', 'statistical', 'maximum', 'minimum')
hogg	('sample', 'craig', 'sample', 'craig', 'sample', 'craig', 'statistic', 'craig', 'median', 'craig')
craig	('hogg', 'hogg', 'hogg', 'hogg', 'hogg', 'probability', 'see', 'kenney')
rank	('midrange', 'mode', 'percentile', 'quantile', 'percentile', 'quantile', 'quantile', 'quantile', 'percentile', 'plotting', 'quartile', 'either', 'statistical', 'median', 'number', 'statistical', 'zipf', 'based', 'estimate', 'test', 'statistic', 'spearman', 'correlation', 'distribution-free', 'statistic', 'spearman', 'correlation', 'spearman', 'correlation', 'spearman', 'spearman', 'correlation', 'spearman', 'correlation', 'coefficient', 'statistical', 'difference', 'smallest', 'signed', 'test', 'median', 'data', 'signed', 'test', 'test', 'spearman', 'correlation', 'statistical', 'statistical', 'signed', 'test', 'statistical', 'statistical', 'statistic', 'test', 'spearman', 'correlation', 'wilcoxon', 'sum', 'signed', 'test', 'trimean', 'trimean', 'statistic', 'spearman', 'correlation', 'spearman', 'correlation', 'matrix', 'matrix', 'signed', 'test', 'signed', 'test', 'wilcoxon', 'sum', 'signed', 'test')
observations	('set', 'most')
occurring	('most', 'time', 'prior', 'event', 'certain', 'number', 'zero', 'event', 'based', 'event')
left	('set', 'far', 'above', 'lie', 'q8', 'distribution', 'tail', 'vanishes', 'gaussian', 'numerical', 'tritetrahedron', 'figure', 'number', 'quantities', 'binomial', 'step', 'difference', 'right', 'above', 'figure;', 'probability', 'bounce', 'right', 'peg')
unique	('histogram', 'mode', 'single', 'maxima', 'single', 'symmetric', 'th', 'symmetric', 'number', 'natural', 'inverse', 'column', 'test', 'answer', 'sklar')
similarly	('data', 'quartile', 'denoted', 'function', 'multivariate', 'discrete', 'function', 'multivariate', 'function', 'expected', 'bivariate', 'authors', 'probability', 'probability', 'probability', 'probability', 'one', 'self-avoiding', 'tetrahedron', 'linear', 'probability', 'distribution', 'central', 'integration', 'poisson', 'distribution', 'multivariate', 'survival')
right	('set', 'decimal', 'decimal', 'added', 'side', 'pronounced', 'tail', 'tail', 'curve', 'curve', 'plot', 'octahedron', 'probability', 'number', 'ways', 'step', 'step', 'mean', 'cross', 'left', 'normal', 'above', 'above', 'bounce', 'left', 'equal', 'taken')
empirical	('data', 'relationship', 'inverted', 'inverted', 'cdf', 'q1', 'distribution', 'et', 'relationship', 'list', 'relationship', 'number')
relationship	('empirical', 'sample', 'two', 'empirical', 'empirical', 'sample', 'factor', 'sum', 'recursion', 'involving', 'functional', 'exact', 'probability', 'occurred', 'functional', 'two', 'strength')
appears	('mode', 'hold', 'phenomenon', 'violate', 'mode', 'hold', 'mode', 'hold')
hold	('appears', 'unimodal', 'appears', 'unimodal', 'appears', 'unimodal', 'independent', 'results', 'sum', 'sequence', 'feller', 'lyapunov')
moderate	('curve', 'asymmetry', 'curve', 'asymmetry', 'curve', 'asymmetry')
basis	('p', 'definition', 'p', 'definition', 'p', 'definition')
three	('one', 'possessing', 'equivalent', 'distribution', 'through', 'dice', 'landing', 'tht', 'least', 'different', 'least', 'sixes', 'lottery', 'plot', 'below', 'random', 'no', 'most-visited', 'polygon', 'choice', 'case', 'unknown', 'calculating', 'essentially', 'one', 'essentially', 'product', 'normal')
outlier	('observation', 'presence', 'indicates', 'convenient', 'definition', 'point', 'influence', 'statistical', 'presence', 'within', 'explicit', 'indicated')
observation	('outlier', 'q3', 'numberer', 'quantile', 'numbered', 'been', 'distribution', 'random', 'p', 'likely', 'calculate', 'estimate', 'procedure', 'nonparametric', 'well', 'calculate', 'prediction', 'mere', 'remains', 'above', 'tells', 'th', 'technique', 'many', 'real', 'within', 'th', 'within', 'within', 'restricted', 'calculate', 'pure', 'real', 'function', 'real', 'two', 'th', 'random', 'z', 'data', 'population', 'experiment', 'order')
overall	('outside', 'pattern', 'significantly-increased', 'influence', '◇', 'quality')
pattern	('overall', 'distribution', 'planar', 'probably')
moore	('distribution', 'mccabe', 'et', 'mccabe', 'excess', 'kurtosis', 'graph', 'inverse', 'penrose', 'inverse', 'penrose', 'independently', 'penrose', 'inverted', 'penrose', 'regression', 'penrose', 'fitting', 'penrose', 'inverse', 'penrose')
mccabe	('moore', 'presence', 'moore', 'mendenhall')
presence	('mccabe', 'outlier', 'outlier')
indicates	('outlier', 'sort')
sort	('indicates', 'index', 'value')
fit	('case', 'model', 'particularly', 'root', 'form', 'data', 'increasingly', 'property', 'using', 'based', 'quite', 'determining', 'type', 'initial', 'nonlinear', 'poor', 'best', 'lead', 'quality', 'parameterized', 'functional', 'value', 'greater', 'curve', 'computed', 'curve', 'computed', 'using', 'based', 'square', 'writing', 'polynomial', 'solved', 'most', 'square', 'noisy', 'curve', 'solution', 'test', 'parabola', 'through', 'cars', 'without')
model	('fit', 'under', 'hazen', 'popular', 'distribution', 'very', 'extended', 'reduces', 'linear', 'due', 'networks', 'unknown', 'data', 'data', 'neelamkavil', 'based', 'always', 'assumes', 'form', 'subject', 'fitting', 'particular', 'calculate', 'nested', 'one', 'indicate', 'probably', 'spread', 'saslaw', 'observed')
study	('error', 'quarter', 'mathematical', 'net', 'riemann', 'common', 'dna', 'variety', 'sampling', 'distribution', 'integer', 'distribution', 'half-integer', 'laplace', 'measurement')
outliers	('measurement', 'easy', 'quartile', 'occur', 'data', 'type', 'discard', 'before', 'true', 'along')
easy	('outliers', 'spot')
spot	('easy',)
figure	('above', 'number', 'significant', 'quantities', 'determined', 'significant', 'quantities', 'above', 'tosses', 'shown', 'square', 'shortening', 'above', 'tile', 'region', 'disk', 'shown', 'shown', 'triangular', 'shown', 'hexagonal', 'left', 'polyhedron', 'merit', 'ogive', 'goals', 'mitrofanova', 'above')
convenient	('outlier', 'definition', 'many', 'most', 'numerical')
times	('fall', 'interquartile')
type	('outliers', 'easily', 'independent', 'stochastic', 'statistic', 'property', 'iii', 'pearson', 'iii', 'skewness', 'multivariate', 'nonparametric', 'different', 'first', 'wagering', 'distinguish', 'number', 'matrix', 'size', 'particular', 'probabilistic', 'pseudoinverse', 'fit', 'particular', 'matrix', 'general', 'pseudoinverse', 'common', 'regression', 'one', 'indistinguishable', 'object', 'two', 'two', 'contain', 'indices', 'chart', 'simple', 'plot', 'plot', 'journal', 'article', 'statistic', 'i', 'error', 'ii', 'test', 'i', 'error', 'ii', 'p-value', 'data', 'test', 'i', 'error', 'ii', 'error', 'error', 'i', 'measurement', 'ii', 'specificity', 'i', 'error', 'ii', 'hypothesis', 'i', 'test', 'ii', 'hypothesis', 'ii', 'test', 'i', 'general', 'statistical', 'pearson', 'iii', 'fisher-tippett', 'common', 'i', 'gumbel', 'general', 'statistical', 'fisher-tippett', 'common', 'i', 'gumbel', 'generalizing', 'pearson', 'iii', 'pearson', 'iv', 'based', 'geometric', 'definition')
identified	('easily', 'scatter', 'through')
scatter	('identified', 'fitting', 'diagram', 'point', 'emphasized', 'random')
diagram	('performing', 'scatter', 'multiplying', 'plane', 'polyhedron', 'plane', 'resembles', 'leaf', 'leaf', 'stem-and-leaf', 'plot', 'quickly', 'column', 'order', 'invented', 'leaf', 'statistical', 'leaf')
squares	('least', 'least', 'fitting')
best	('data', 'discard', 'line', 'finite', 'choose', 'finding', 'fitting', 'find', 'fit', 'value', 'satisfy', 'point', 'critical')
discard	('best', 'outliers')
before	('outliers', 'computing', 'computed', 'normal', 'air', 'upward', 'toss', 'encountered', 'seeing', 'seeing', 'thth', 'tthh', 'thhh', 'coin', 'first', 'state', 'cards', 'step', 'first', 'see', 'nonlinear', 'raw', 'failure', 'first', 'failure', 'th')
particularly	('fit', 'true', 'displacements', 'brownian', 'function', 'simple', 'based', 'important')
true	('particularly', 'outliers', 'meaning', 'value', 'meaning', 'value', 'value', 'estimator', 'special', 'peakedness', 'general;', 'variance', 'th', 'mean', 'differ', 'probability', 'bonferroni', 'remains', 'even', 'independent', 'derived', 'deviation', 'transpose', 'shortest', 'usual', 'smaller', 'frequency', 'distribution', 'assumption', 'test', 'test', 'positive', 'positive', 'statistic', 'name', 'positive', 'sensitivity', 'negative', 'test', 'hypothesis', 'uncorrelated', 'uspensky', 'probability', 'deviation', 'population', 'trial', 'probability')
along	('outliers', 'concentration', 'real', 'point', 'factor', 'taken', 'taken', 'point', 'incorporated', 'point', 'incorporated')
greatly	('point', 'influence', 'vary', 'dimension', 'convergence', 'improved')
influence	('greatly', 'outlier', 'overall')
fitting	('squares', 'scatter', 'other', 'square', 'linear', 'original', 'square', 'regression', 'provide', 'function', 'form', 'addition', 'technique', 'square', 'technique', 'best', 'square', 'independently', 'number', 'square', 'applied', 'square', 'proceeds', 'square', 'regression', 'square', 'exponential', 'square', 'logarithmic', 'square', 'perpendicular', 'square', 'polynomial', 'square', 'power', 'square', 'pseudoinverse', 'solving', 'square', 'exponential', 'square', 'least', 'square', 'logarithmic', 'square', 'power', 'least', 'square', 'logarithmic', 'square', 'least', 'square', 'exponential', 'square', 'power', 'provide', 'function', 'form', 'square', 'perpendicular', 'square', 'point', 'square', 'polynomial', 'square', 'vandermonde', 'square', 'power', 'square', 'least', 'square', 'exponential', 'square', 'logarithmic', 'least', 'square', 'square', 'least', 'square', 'polynomial', 'square', 'regression', 'data', 'model', 'square', 'regression', 'square', 'matrix', 'square', 'multivariate', 'square', 'square', 'regression', 'square', 'linear', 'square', 'moore', 'square', 'normal', 'method', 'curve', 'square', 'linear', 'square', 'recursion', 'regression', 'square', 'square', 'manova', 'pp', 'one-parameter', 'square', 'maximum')
percentile	('th', 'value', 'size', 'descriptive', 'statistic', 'rank', 'statistic', 'statistic', 'rank', 'parametrized', 'statistic', 'statistic', 'rank', 'range', 'quantile')
say	('value', 'cumulative', 'value', 'cumulative', 'player', 'th', 'line', 'plotting', 'look', 'sequence', 'journal', 'either')
quantities	('list', 'number', 'less', 'addition', 'division', 'dividing', 'exponentiation', 'logarithm', 'multiplication', 'number', 'less', 'numerical', 'only', 'two', 'equal', 'figure', 'figure', 'set', 'absolute', 'remaining', 'computed', 'matrix', 'covariance', 'statistical', 'set', 'relative', 'tile', 'tile', 'tile', 'tile', 'left', 'examine', 'two', 'linearly', 'mean', 'unnormalized', 'two', 'graphed', 'variance', 'interpreted', 'term', 'matrix', 'definition', 'connected', 'set', 'set', 'statistical', 'determined', 'excess', 'distribution')
list	('quantities', 'median', 'data', 'normal', 'mean', 'data', 'empirical', 'mean', 'data', 'deviation', 'deviation', 'data', 'physical', 'confidence', 'variance', 'data', 'square', 'shuffling', 'find', 'triangle', 'value', 'arranged', 'element', 'element', 'example', 'run-length')
quantity	('below', 'know', 'kenney', 'value', 'actual', 'degree', 'correct', 'example', 'specified', 'range', 'specified', 'difference', 'fixed', 'difference', 'estimated', 'error', 'error', 'unknown', 'outcome', 'value', 'measured', 'numerical', 'together', 'example', 'four', 'rounding', 'significant', 'indicating', 'exhibit', 'derived', 'statistical', 'refers', 'root-mean-square', 'mean', 'analogous', 'function', 'deviation', 'use', 'implicitly', 'kenney', 'out', 'chi-squared', 'work', 'process', 'provided', 'element', 'statistical', 'correlation', 'quality', 'unfortunately', 'because', 'appropriate', 'term', 'correlation', 'variance', 'always', 'period', 'period', 'period', 'period', 'period', 'period', 'period', 'initial', 'period', 'period', 'period', 'period', 'period', 'period', 'period', 'period', 'frequencies', 'measure', 'test', 'probability', 'confidence', 'statistical', 'difference', 'positive', 'feller')
position	('quantile-quantile', 'plotting', 'descriptive', 'q7', 'q9', 'approximately', 'plotting', 'probability', 'computing', 'first', 'apart', 'needle', 'cards', 'cards', 'most', 'cards', 'cards', 'exchange', 'above', 'complex', 'plotting', 'quantile')
quantile-quantile	('position', 'q9', 'same')
compares	('plot', 'observed')
determined	('distribution', 'evaluating', 'estimate', 'figure', 'smallest', 'probabilities', 'most', 'storing', 'uniquely', 'spanning', 'segment', 'uniquely', 'description', 'quantities', 'sample', 'sample')
evaluating	('determined', 'quantile', 'integral')
positions	('plotting',)
distinct	('number', 'closely', 'two', 'number', 'stochastic', 'matrices', 'nonsingular', 'number', 'minimal', 'two', 'notions', 'two', 'total', 'term', 'distribution')
closely	('distinct', 'precision', 'precision', 'function', 'approximated', 'function', 'gamma', 'distribution', 'other')
finite	('statistic', 'actually', 'transitions', 'markov', 'moment', 'series', 'distribution', 'first', 'occurrence', 'number', 'probability', 'number', 'coin', 'thickness', 'player', 'number', 'rewritten', 'either', 'dollars', 'amount', 'almost', 'set', 'indication', 'number', 'variate', 'best', 'critical', 'critical', 'term', 'distribution', 'term', 'mean', 'central')
existing	('actually', 'group')
possibly	('objects', 'positive', 'eigenvalue', 'process', 'random')
large	('enumerated', 'indefinitely', 'total', 'become', 'kenney', 'mean', 'tail', 'end', 'equally', 'number', 'average', 'mosteller', 'number', 'truly', 'expected', 'payoff', 'balanced', 'amount', 'law', 'symmetric', 'selection', 'set', 'generator', 'matrix', 'order', 'matrix', 'real', 'one', 'law', 'law', 'odd', 'shown', 'disproportionately', 'law', 'frequency', 'unwieldy', 'successes', 'approximately', 'probability', 'first', 'product', 'number', 'sum', 'number', 'case', 'a014481', 'distribution', 'expanding', '◇', 'use', 'sufficiently', 'weak', 'law', 'distribution', 'distribution', 'cars', 'oeis', 'one', 'law', 'law', 'law', 'enough', 'absolutely', 'truly', 'law', 'feller', 'law', 'law', 'law', 'law', 'truly', 'law', 'law', 'law', 'truly', 'law')
enumerated	('large', 'theory', 'guttmann')
theory	('enumerated', 'people', 'score', 'estimation', 'excess', 'probability', 'mean', 'function', 'point', 'log', 'classical', 'modified', 'percolation', 'percolation', 'distribution', 'distribution', 'distribution', 'van', 'matrix', 'cited', 'number', 'film', 'point', 'distribution', 'important', 'distribution', 'random', 'basic', 'stochastic', 'percolation', 'random', 'percolation', 'site', 'run', 'percolation', 'prediction', 'time', 'sampling', 'time', 'prediction', 'random', 'based', 's-systems', 'feller', 'probability', 'bernoulli')
people	('theory', 'living', 'out', 'two', 'out', 'no', 'out', 'probability', 'shared', 'number', 'least', 'number', 'obtain', 'number', 'probability', 'number', 'value', 'number', 'two', 'who', 'number', 'get', 'two', 'picked', 'practice', 'willing')
living	('people', 'united')
united	('living', 'generalization', 'september', 'states;', 'index', 'consumer', 'year', 'alone')
generalization	('united', 'experience', 'distribution', 'bivariate', 'further', 'throwing', 'topological', 'meaning', 'variate', 'concept', 'multivariate', 'student', 'function', 'poisson')
experience	('generalization', 'indefinitely')
indefinitely	('experience', 'large', 'probability')
throws	('number', 'might', 'set', 'regarded', 'number', 'double-six', 'two')
might	('throws', 'conceivably', 'joined', 'ambiguity', 'net', 'fold', 'distance', 'seem')
conceivably	('might', 'unlimited')
unlimited	('conceivably', 'time')
time	('unlimited', 'particular', 'relative', 'relative', 'likelihood', 'expectation', 'no', 'set', 'subscript', 'shoots', 'bullet', 'attempt', 'series', 'point', 'occurring', 'prior', 'function', 'intensity', 'constant', 'intensity', ';', 'present', 'worth', 'process', 'series', 'finch', 'recursive', 'tosses', 'only', 'paulos', 'spend', 'air', 'likely', 'likely', 'around', 'history', 'prior', 'prior', 'strictly', 'prior', 'conditional', 'function', 'series', 'process', 'series', 'earliest', 'objects', 'probability', 'function', 'series', 'function', 'series', 'immigrant', 'series', 'function', 'series', 'measure', 'series', 'process', 'series', 'mark', 'series', 'space', 'series', 'sequence', 'process', 'series', 'process', 'series', 'over', 'random', 'one-by-one', 'evolves;', 'process', 'series', 'set', 'series', 'follow', 'player', 'process', 'series', 'process', 'series', 'either', 'point', 'process', 'series', 'represent', 'location', 'process', 'series', 'process', 'series', 'shoots', 'bullet', 'isolated', 'set', 'parameters;', 'process', 'series', 'continuous', 'random', 'identity', 'minimum', 'increments', 'under', 'general', 'dependent', 'nonoverlapping', 'different', 'interquartile', 'interquartile', 'value', 'series', 'average', 'series', 'average', 'series', 'dependent', 'index', 'nonstationary', 'series', 'series', 'series', 'predictability', 'future', 'predictability', 'series', 'theory', 'series', 'deterministic', 'series', 'redundancy', 'series', 'average', 'series', 'theory', 'series', 'effect', 'series', 'smoothing', 'series', 'average', 'series', 'formula', 'series', 'ordered', 'data', 'interval', 'example', 'series', 'goals', 'series', 'castiglioni', 'series', 'analysis', 'series', 'uncorrelated', 'series', 'number', 'series', 'procedure', 'number', 'series', 'series', 'whenever', 'probabilistic', 'intension', 'doob', 'th', 'successive', 'poisson', 'th', 'th', 'integer', 'survival', 'bacteria', 'one', 'ball', 'absolute', 'papoulis', 'possible')
dice	('actual', 'three', 'rolled', 'number', 'coin', 'gambler', 'french', 'two', 'thrown', 'boxcars', 'newton', 'set', 'six', 'sixes', 'sixes', 'roll', 'regularized', 'problem', 'gambler')
regarded	('throws', 'incorrectly', 'measure', 'processes', 'archetypal')
drawn	('sample', 'practically', 'sample', 'normal', 'sample', 'normal', 'ball', 'urn')
practically	('drawn', 'infinite')
purely	('population', 'hypothetically', 'value', 'normally')
hypothetically	('purely', 'population')
completely	('population', 'described', 'two', 'different', 'interval', 'independent', 'authors', 'separate', 'error', 'statistic', 'different', 'under', 'different', 'size', 'dropped', 'use', 'different')
described	('completely', 'process', 'still', 'jumps', 'levy', 'nolan', 'index')
mathematically	('population',)
no	('quantile', 'fewer', 'sense', 'other', 'process', 'time', 'definition', 'reference', 'general', 'closed-form', 'estimation', 'meaningful', 'expectation', 'parametric', 'probability', 'two', 'shared', 'people', 'data', 'trace', 'probability', 'two', 'probability', 'consecutive', 'meaningfully', 'apparent', 'element', 'divisors', 'occur', 'reason', 'formulating', 'reason', '$2', 'matter', 'showing', 'independent', 'proven', 'three', 'corner', 'two', 'probability', 'consecutive', 'proportion', 'longer', 'consideration', 'single', 'small', 'exact')
fewer	('no', 'two', 'indication', 'one')
evans	('denoted', 'et', 'p', 'et', 'enough', 'et', 'function', 'et', 'denoted', 'et', 'et', 'space', 'et', 'denoted', 'et', 'sample', 'et', 'analysis', 'et', 'p', 'et', 'distribution', 'et', 'table', 'et', 'denoted', 'et', 'p', 'et', 'denoted', 'et', 'number', 'et')
ties	('close', 'quantile')
assigns	('function', 'probability')
attained	('probability', 'certain', 'probability', 'value')
certain	('attained', 'probability', 'subject', 'branching', 'occurring', 'probability', 'obey', 'relation', 'fixed', 'satisfying', 'uniformity', 'satisfying', 'general', 'wigner', 'special', 'directions', 'event', 'subset', 'consisting', 'based', 'set', 'mean', 'statistic')
parametrized	('percentile', 'version')
d	('returns', 'statistic', 'statistic')
returns	('d', 'th')
floor	('statistic', 'line', 'grid', 'line', 'equally', 'cover', 'regularly', 'vary', 'coefficient', 'distribution')
ceiling	('function', 'equation')
fractional	('function', 'accuracy', 'part')
part	('number', 'important', 'fractional', 'integer', 'integer', 'least', 'characteristic', 'first', 'second', 'vital', 'modern')
slightly	('number', 'different', 'distribution', 'though', 'principle', 'wider', 'line', 'expression', 'coin', 'likely', 'die', 'higher', 'archaic', 'p', 'different', 'p', 'smaller', 'other', 'different', 'segment', 'separated', 'series', 'shifted', 'excess', 'use', 'different', 'function', 'different', 'elementary', 'cumbersome')
#	('plotting',)
q1	('inverted', 'empirical', 'same', 'except')
inverted	('q1', 'empirical', 'q2', 'empirical', 'long', 'expanding', 'numerically', 'well', 'moore')
q2	('inverted', 'value', 'essentially')
cdf	('empirical', 'cumulative')
q3	('observation', 'th')
numberer	('observation', 'closest')
closest	('numberer', 'numbered', 'sample', 'value', 'still')
q4	('california', 'interpolation')
california	('q4', 'department')
department	('california', 'public')
public	('department',)
q5	('hazen',)
hazen	('q5', 'model')
popular	('model',)
q6	('weibull', 'vertices')
weibull	('q6', 'proposed', 'distribution', 'distribution', 'distribution', 'two-parameter', 'distribution', 'statistic', 'distribution', 'distribution', 'distribution', 'distribution', 'form', 'distribution', 'distribution', 'involving', 'distribution')
q7	('interpolation', 'position')
interpolation	('q7', 'q4', 'coefficient', 'least')
q8	('unbiased', 'left')
q9	('approximate', 'position', 'quantile-quantile')
approximate	('q9', 'unbiased', 'arithmetic', 'numerical', 'exist', 'distribution', 'continuous', 'heaps', 'normal')
normal	('estimate', 'plot', 'list', 'interval', 'measurement', 'distribution', 'mean', 'distribution', 'erf', 'distribution', 'error', 'parent', 'moment', 'distribution', 'rearranging', 'weighted', 'integral', 'distribution', 'bivariate', 'distribution', 'because', 'distribution', 'kenney', 'log', 'distribution', 'before', 'p', 'population', 'log', 'distribution', 'under', 'moment', 'distribution', 'population', 'distribution', 'reference', 'log', 't', 'bivariate', 'distribution', 'bivariate', 'distribution', 'bivariate', 'distribution', 'independent', 'below', 'bivariate', 'probability', 'bivariate', 'distribution', 'bivariate', 'distribution', 'bivariate', 'distribution', 'bivariate', 'distribution', 'multivariate', 'distribution', 'distribution', 'distribution', 'trivariate', 'distribution', 'multivariate', 'distribution', 'multivariate', 'distribution', 'multivariate', 'distribution', 'bivariate', 'distribution', 'multivariate', 'distribution', 'multivariate', 'multivariate', 'distribution', 'bivariate', 'distribution', 'theorem', 'distribution', 'trivariate', 'distribution', 'multivariate', 'trivariate', 'distribution', 'trivariate', 'distribution', 'bivariate', 'distribution', 'multivariate', 'distribution', 'distribution', 'distribution', 'multivariate', 'example', 'standard', 'function', 'bivariate', 'complex', 'below', 'bivariate', 'distribution', 'distribution', 'deviate', 'deviate', 'distribution', 'standard', 'close', 'standard', 'standard', 'standard', 'two-dimensional', 'shuffle', 'shuffling', 'standard', 'number', 'distribution', 'bivariate', 'distribution', 'bivariate', 'distribution', 'approximately', 'kenney', 'bivariate', 'distribution', 'still', 'using', 'equation', 'equation', 'right', 'equation', 'because', 'range', 'range', 'matrix', 'equation', 'fitting', 'matrix', 'inverse', 'equation', 'same', 'deck', 'approximately', 'need', 'distribution', 'series', 'distribution', 'standard', 'distribution', 'error', 'drawn', 'universe', 'drawn', 'universe', 'two', 'test', 'distribution', 'most', 'statistic', 'distribution', 'approximately', 'bivariate', 'distribution', 'variate', 'distribution', 'distribution', 'half', 'distribution', 'variate', 'distribution', 'distribution', 'variate', 'distribution', 'distribution', 'half', 'distribution', 'distribution', 'distribution', 'bivariate', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'variance', 'distribution', 'distribution', 'distribution', 'distribution', 'variate', 'distribution', 'difference', 'distribution', 'distribution', 'variate', 'distribution', 'product', 'distribution', 'ratio', 'distribution', 'sum', 'variable', 'log', 'distribution', 'log', 'distribution', 'standard', 'distribution', 'distribution', 'distribution', 'half', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'flight', 'distribution', 'variable', 'log', 'distribution', 'log', 'distribution', 'same', 'log', 'distribution', 'log', 'log', 'distribution', 'log', 'distribution', 'distribution', 'distribution', 'function', 'variance', 'difference', 'distribution', 'distribution', 'distribution', 'ratio', 'distribution', 'sum', 'distribution', 'developed', 'distribution', 'p', 'distribution', 'standard', 'general', 'arbitrary', 'distribution', 'standard', 'two', 'variance', 'distribution', 'standard', 'variate', 'approximated', 'distribution', 'case', 'integral', 'function', 'physics', 'tend', 'roughly', 'invoke', 'properties', 'distribution', 'distribution', 'sum', 'distribution', 'difference', 'independent', 'normal!', 'ratio', 'variance', 'distribution', 'function', 'distribution', 'function', 'distribution', 'distribution', 'case', 'distribution', 'p', 'variate', 'distribution', 'number', 'distribution', 'equation', 'distribution', 'system', 'distribution', 'distribution', 'distribution', 'bivariate', 'distribution', 'half', 'distribution', 'transformation', 'deviate', 'deviate', 'distribution', 'function', 'product', 'distribution', 'ratio', 'distribution', 'sum', 'standard', 'distribution', 'cumulative', 'probability', 'variate', 'different', 'distribution', 'variate', 'distribution', 'function', 'distribution', 'three', 'blue', 'product', 'distribution', 'difference', 'distribution', 'distribution', 'distribution', 'ratio', 'distribution', 'sum', 'bivariate', 'function', 'ratio', 'distribution', 'difference', 'distribution', 'distribution', 'distribution', 'product', 'distribution', 'sum', 'respectively', 'distribution', 'variate', 'cramer', 'theorem', 'sum', 'theorem', 'difference', 'distribution', 'distribution', 'distribution', 'product', 'distribution', 'ratio', 'equation', 'curve', 'bivariate', 'bivariate', 'distribution', 'universe', 'distribution', 'erf', 'distribution', 'standard', 'distribution', 'standard', 'distribution', 'distribution', 'standard', 'standard', 'distribution', 'erf', 'distribution', 'distribution', 'distribution', 'become', 'student', 'analog', 'defining', 'approximated', 'distribution', 'distribution', 'approximate', 'distribution', 'distribution', 'log', 'distribution', 'example', 'distribution', 'standard', 'distribution', 'variance', 'form', 'function', 'feller', 'conversion', 'form', 'variate', 'distribution', 'theorem', 'distribution', 'independent', 'standardized', 'tend', 'condition', 'distribution', 'condition', 'distribution')
language	('parametrization', 'probability', 'cannot', 'machine', 'function', 'package', 'numerical', 'wolfram', 'significance', 'application', 'prior', 'prior', 'prior', 'package', 'package', 'package', 'command', 'code', 'most', 'function', 'run', 'chernoff', 'appropriate', 'package', 'package', 'package', 'package', 'function', 'package', 'package')
parametrization	('language', 'handle', 'rimmer')
handle	('parametrization', 'basket')
estimated	('function', 'cumulative', 'quantity', 'measured', 'together', 'mean', 'sample', 'root', 'error', 'actually', 'data', 'mean', 'sample', 'point', 'seeing', 'probability', 'latter', 'et', 'probability', 'unit', 'relative')
specified	('set', 'quantity', 'quantity', 'uniquely', 'table', 'class', 'uniquely', 'processes', 'needle', 'space', 'triple', 'number', 'chance', 'distribution', 'over', 'within', 'range', 'other', 'arranged', 'order')
essentially	('q2', 'same', 'statistic', 'because', 'motion', 'sausage-like', 'a001083', 'one', 'three', 'three', 'interval', 'limit')
numbered	('observation', 'closest', 'row', 'path')
vertices	('q6', 'divide', 'graph', 'minimal', 'one', 'midpoint')
regions	('probability', 'track')
proposed	('average', 'weibull', 'statistic', 'spearman', 'et', 'flipping', 'first', 'nicolaus', 'originally', 'quantify')
four	('one', 'divisions', 'grouped', 'equal-sized', 'quantity', 'landing', 'one', 'math', 'testing', 'repeated', 'savageau', 'free')
divisions	('four',)
equal-sized	('four',)
top	('including', 'statistically', 'flat', 'infinite', 'initial', 'side', 'toss', 'opposite', ';', 'curve', 'series')
ranked	('members',)
members	('ranked', 'first', 'number', 'bin', 'bin', 'number', 'sample', 'sample', 'number', 'sample', 'sample', 'distribution', 'high')
denotes	('table', 'nearest', 'error', 'distribution', 'expectation', 'mean', 'expectation', 'distribution', 'th', 'function', 'expectation', 'namely', 'mean', 'moment', 'value', 'moment', 'expectation', 'mean', 'expectation', 'matrix', 'matrix', 'probability', 'inequality', 'disjoint', 'exist', 'rewritten', 'little-o', 'set', 'lebesgue', 'symbolically', 'expected', 'weight', 'complement', ';', 'probability', 'irrelevant', 'subset', 'cardinality', 'written', 'function', 'subset', 'self-correcting', 'self-exciting', 'a078416', 'matrix', 'motion', 'open', 'correlation', 'standard', 'iff', 'proper', 'zabell', 'expectation')
integer	('nearest', 'bits', 'general', 'general', 'arithmetic', 'floating-point', 'part', 'part', 'nearest', 'function', 'papoulis', 'mod', 'joint', 'schoenberg', 'transylvania', 'law', 'matrix', 'matrix', 'wolfram', 'binomial', 'binomial', 'consistent', 'study', 'spin', 'distribution', 'defining', 'distribution', 'time', 'first', 'oeis', 'probability', 'lattice', 'geometric', 'memoryless')
minitab	('tukey',)
hoaglin	('tukey', 'et')
mendenhall	('mccabe', 'sincich', 'distribution', 'sincich')
sincich	('mendenhall', 'freund', 'mendenhall', 'raw')
freund	('sincich', 'perles')
perles	('freund', 'quartile')
variation	('quartile', 'coefficient', 'quartile', 'coefficient', 'quartile', 'coefficient', 'bounded', 'interval', 'bounded', 'interval', 'mean', 'coefficient', 'coefficient', 'coefficient', 'p', 'extended', 'additional', 'chance', 'identify')
regression	('mean', 'mean', 'mentions', 'local', 'nonparametric', 'local', 'local', 'linear', 'statistical', 'logit', 'assumes', 'logit', 'logit', 'correlation', 'autocorrelation', 'complete', 'coefficient', 'correlation', 'fitting', 'coefficient', 'population', 'distribution', 'correlation', 'correlation', 'estimate', 'line', 'index', 'correlation', 'coefficient', 'ratio', 'correlation', 'coefficient', 'coefficient', 'function', 'merit', 'technique', 'square', 'vertical', 'fitting', 'anova', 'pseudoinverse', 'coefficient', 'exponential', 'least', 'logarithmic', 'least', 'offset', 'least', 'polynomial', 'least', 'law', 'least', 'linear', 'linear', 'least', 'linear', 'linear', 'linear', 'least', 'multiple', 'nonlinear', 'fitting', 'inverse', 'drazin', 'function', 'linear', 'linear', 'least', 'fitting', 'polynomial', 'elliptic', 'inverse', 'drazin', 'conditional', 'multiple', 'multiple', 'least', 'fitting', 'least', 'linear', 'moore', 'equation', 'least', 'pseudoinverse', 'matrix', 'type', 'linear', 'term', 'term', 'recursion', 'recursion', 'fractal', 'linear', 'merit', 'multiple', 'nonlinear', 'recursion', 'coefficient', 'fitting', 'coefficient', 'coefficient', 'coefficient', 'correlation', 'residual', 'residual', 'correlation', 'covariance', 'covariance')
reversion	('statistic', 'mean', 'mean', 'mean', 'mean', 'mean', 'constant')
stating	('phenomenon', 'greater')
next	('probability', 'measured', 'manner', 'point', 'manner', 'point', 'require', 'block', 'mean', 'row', 'appropriate')
deviate	('variate', 'less', 'normal', 'normal', 'normal', 'normal')
extreme	('word', 'event', 'less', 'function', 'confusion', 'care', 'distribution', 'value', 'confusion', 'care', 'statistic', 'value', 'equivalently', 'case', 'whisker', 'data', 'distribution', 'value', 'distribution', 'value', 'fisher-tippett', 'value', 'distribution', 'order', 'maximum', 'value', 'distribution', 'value', 'beta', 'value', 'distribution', 'value', 'fisher-tippett', 'value', 'distribution', 'order', 'minimum', 'value', 'distribution', 'value', 'distribution', 'value')
followed	('likely', 'less', 'walk', 'random', 'distribution', 'square')
violate	('appears', 'definition', 'approach', 'implicit')
reflects	('event', 'fact')
nonnegative	('definition', 'over', 'restricted', 'grid', 'restricted', 'grid', 'matrices', 'constant', 'levy', 'function')
integrates	('interval', 'one')
you	('interval', 'move', 'mean', 'increases', 'longer', 'suppose', 'measuring', 'continuous', 'wish')
move	('you', 'away')
away	('move',)
closer	('lie', 'mean')
formally	('season', 'order', 'set', 'net', 'distribution')
sniper	('episode',)
mentions	('numb3rs', 'regression')
score	('function', 'matrix', 'function', 'theory', 'function', 'z', 'statistical')
derivative	('log-likelihood', 'probability', 'expectation', 'partial', 'probability', 'term', 'remove', 'remove', 'replace', 'distribution', 'cannot', 'minimizing', 'again', 'construct', 'distribution', 'gram-charlier', 'distribution', 'density', 'direct', 'exist', 'distribution')
log-likelihood	('derivative', 'function', 'notation', 'function')
defining	('function', 'likelihood', 'variance', 'computed', 'solving', 'line', 'number', 'particular', 'likelihood', 'symbolically', 'quantile', 'form', 'side', 'integer', 'simplifies', 'computed', 'raw', 'mechanics', 'boltzmann', 'using', 'probability', 'normalized', 'normal', 'p', 'characteristic', 'coefficient', 'fisher')
formulation	('above', 'one', 'order', 'cannot', 'original', 'lacked')
variance	('precisely', 'probability', 'dispersion', 'deviation', 'estimate', 'ratio', 'mean', 'mean', 'digit', 'estimator', 'sample', 'unbiased', 'fisher', 'minimum', 'minimum', 'th', 'first', 'population', 'estimator', 'sample', 'sample', 'sample', 'written', 'sample', 'sample', 'authors', 'sample', 'unbiased', 'distinction', 'sample', 'sample', 'sample', 'computation', 'sample', 'distribution', 'estimator', 'deviation', 'expectation', 'noted', 'sample', 'sample', 'original', 'moment', 'motivates', 'standard', 'sum', 'correlation', 'transformations', 'estimator', 'heteroscedastic', 'homoscedastic', 'homoscedastic', 'form', 'trimean', 'square', 'deviation', 'standard', 'moment', 'true', 'population', 'sample', 'robbin', 'median', 'sample', 'first', 'defining', 'sample', 'computation', 'sample', 'sample', 'sample', 'distribution', 'distribution', 'sample', 'sample', 'sample', 'kenney', 'variable', 'depend', 'sample', 'distribution', 'sample', 'sample', 'sample', 'computation', 'distribution', 'kendall', 'equal', 'set', 'bias-corrected', 'standard', 'sample', 'sample', 'sample', 'distribution', 'error', 'moment', 'unbiased', 'sample', 'sample', 'sample', 'distribution', 'deviation', 'written', 'population', 'whereas', 'distribution', 'equal', 'symbol', 'example', 'computed', 'above', 'order', 'sample', 'list', 'root', 'standard', 'two', 'sample', 'uncorrected', 'data', 'data', 'variable', 'using', 'matrix', 'sample', 'sample', 'sample', 'computation', 'sample', 'distribution', 'correlation', 'kenney', 'quadrant', 'kurtosis', 'spearman', 'minimum', 'unbiased', 'estimator', 'perlman', 'asymptotic', 'minimum', 'unbiased', 'wishura', 'case', 'asymptotic', 'case', 'verified', 'function', 'mean', 'increments', 'coefficient', 'surface', 'p', 'observed', 'quantities', 'estimator', 'acton', 'variable', 'quantity', 'sum', 'zero', 'matrix', 'run', 'mean', 'higher', 'analysis', 'statistical', 'anova', 'independent', 'replicate', 'mean', 'sample', 'mean', 'sample', 'common', 'distributed', 'residual', 'set', 'bernoulli', 'lexis', 'uspensky', 'sample', 'sampling', 'sample', 'slovin', 'set', 'bernoulli', 'distributed', 'independent', 'smaller', 'second', 'normal', 'distribution', 'normally', 'expressible', 'infinite', 'infinite', 'noncentral', 'noncentral', 'normal', 'statistic', 'normal', 'distribution', 'normal!', 'normal', 'variate', 'sample', 'general', 'delta', 'respectively', 'mean', 'linear', 'derived', 'weighted', 'cramer', 'probability', 'student', 'chi-squared', 'circular', 'von', 'form', 'beta', 'final', 'sample', 'distribution', 'distribution', 'robbin', 'number', 'normal', 'conversion', 'individual', 'distribution', 'unit', 'feller', 'small', 'feller')
extensive	('function',)
pure	('mathematics', 'mathematics', 'observation')
applied	('key', 'root-mean-square', 'two', 'again', 'two', 'correction', 'measured', 'particular', 'most', 'form', 'fitting', 'iteratively', 'offset', 'new', 'most', 'filter')
key	('applied', 'component')
component	('key', 'field', 'leading', 'written', 'form', 'connected', 'percolation', 'take', 'random', 'combined', 'chance')
field	('component', 'likelihood', 'sum', 'practice', 'papoulis', 'consisting')
expectation	('derivative', 'value', 'bias', 'value', 'value', 'variable', 'value', 'multiple', 'value', 'variable', 'value', 'estimator', 'value', 'denotes', 'moment', 'equation', 'equal', 'value', 'time', 'value', 'estimator', 'value', 'variance', 'denotes', 'size', 'notation', 'denotes', 'moment', 'mean', 'eliminating', 'denotes', 'denotes', 'conditional', 'no', 'analysis', 'value', 'toss', 'value', 'conditional', 'equal', 'distributed', 'excess', 'value', 'yield', 'value', 'conditional', 'sample', 'variable', 'setting', 'trial', 'value', 'value', 'selection', 'value', 'indicate', 'denotes', 'zero', 'unit')
logarithm	('function', 'log', 'quantities', 'moment-generating', 'likelihood', 'function', 'natural', 'natural', 'probability', 'variable', 'variable', 'function', 'expanding')
log	('logarithm', 'likelihood', 'distribution', 'normal', 'distribution', 'normal', 'example', 'normal', 'theory', 'likelihood', 'independently', 'likelihood', 'test', 'likelihood', 'ratio', 'likelihood', 'distribution', 'series', 'case', 'normal', 'distribution', 'normal', 'distribution', 'normal', 'reduce', 'normal', 'function', 'normal', 'approximately', 'normal', 'shaw', 'normal', 'distribution', 'series', 'law', 'normal', 'distribution', 'series', 'excess', 'series', 'distribution', 'normal')
signed	('deviation', 'deviation', 'deviation', 'deviation', 'deviation', 'deviation', 'deviation', 'deviation', 'deviation', 'deviation', 'deviation', 'wilcoxon', 'rank', 'wilcoxon', 'rank', 'wilcoxon', 'rank', 'wilcoxon', 'rank', 'wilcoxon', 'rank', 'wilcoxon', 'rank', 'wilcoxon', 'rank')
dispersion	('statistical', 'variance', 'statistical', 'descriptive', 'statistical', 'two')
smallest	('statistical', 'equal', 'number', 'determined', 'significant', 'rank', 'largest', 'birthdays', 'number', 'out', 'number', 'edelman', 'probability', 'function', 'value', 'parameter', 'value', 'polynomial', 'maximum', 'head', 'coin', 'largest', 'order')
up	('either', 'roughly', 'law', 'repeated', 'breaking', 'summand', 'generated', 'present', 'two', 'through', 'face', 'h', 'introduced', 'turns', 'come', 'turn', 'first', 'turn', 'second', 'turn', 'turn', 'third', 'take', 'step', 'walk', 'length', 'set', 'tendency', 'various')
down	('set', 'breaks', 'less', 'human', 'based', 'first', 'ball', 'apex')
depth	('statistical', 'descriptive')
symmetric	('value', 'interval', 'probability', 'unique', 'unbiased', 'unique', 'unbiased', 'statistic', 'covariance', 'definition', 'case', 'large', 'real', 'real', 'random', 'real', 'matrix', 'simple', 'random', 'statistic', 'statistic', 'group', 'mode', 'triangular')
efficient	('most', 'sense', 'less')
sense	('efficient', 'no', 'probability', 'particular', 'talk', 'set', 'function', 'generalized', 'sum', 'sufficiently')
estimating	('statistic', 'smaller')
smaller	('estimating', 'become', 'prescribed', 'slightly', 'true', 'stronger', 'distribution', 'variance', 'freedom', 'observed', 'order', 'ball', 'distance', 'value', 'occur')
efficiency	('p', 'quantization', 'sample', 'sample')
sensitive	('less',)
l-estimate	('press', 'linear', 'order', 'trimean')
press	('l-estimate', 'et', 'mean', 'et', 'median', 'et', 'parameter', 'et')
small	('p', 'very', 'within', 'insensitive', 'departures', 'over', 'stochastic', 'tail', 'end', 'anova', 'data', 'error', 'representative', 'coincidence', 'world', 'introduces', 'degree', 'world', 'common', 'world', 'problem', 'world', 'plane', 'distribution', 'plot', 'first', 'walk', 'computing', 'weight', 'function', 'agreement', 'table', 'oeis', 'relatively', 'data', 'reject', 'form', 'no', 'interval', 'various', 'taken', 'sufficiently', 'interval', 'sufficiently', 'interval', 'many', 'unrelated', 'law', 'variance', 'compared', 'law')
estimator	('range', 'population', 'estimate', 'error', 'error', 'bias', 'exhibits', 'exhibits', 'biased', 'biased', 'biased', 'bias', 'unbiased', 'unbiased', 'rule', 'mean', 'population', 'error', 'error', 'bias', 'variance', 'error', 'estimate', 'bias', 'unbiased', 'true', 'unbiased', 'unbiased', 'bias', 'biased', 'biased', 'biased', 'unbiased', 'unbiased', 'central', 'moment', 'maximum', 'expectation', 'fisher', 'inequality', 'central', 'halmos', 'halmos', 'kenney', 'kenney', 'population', 'unbiased', 'variance', 'm', 'estimate', 'l', 'population', 'bayesian', 'likelihood', 'likelihood', 'value', 'likelihood', 'likelihood', 'maximum', 'actual', 'point', 'point', 'l', 'l', 'population', 'sample', 'kenney', 'population', 'standard', 'sample', 'unbiased', 'variance', 'exhibit', 'unbiased', 'unbiased', 'unbiased', 'unbiased', 'biased', 'biased', 'biased', 'biased', 'bias', 'expectation', 'cumulant', 'unbiased', 'variance', 'population', 'population', 'population', 'skewness', 'kenney', 'moment', 'population', 'population', 'unbiased', 'necessary', 'population', 'point', 'uniformly', 'unbiased', 'variance', 'wishura', 'asymptotic', 'point', 'uniformly', 'unbiased', 'maximum', 'likelihood', 'perlman', 'case', 'buffon', 'buffon', 'asymptotically', 'unbiased', 'number', 'likelihood', 'negative', 'point', 'variance', 'difference', 'random', 'test', 'properties', 'population', 'mean', 'trial', 'probability', 'value', 'indeed', 'population')
violet	('two', 'mean')
initial	('vector', 'point', 'point', 'level', 'intensity', 'landing', 'top', 'probability', 'side', 'above', 'term', 'modulus', 'number', 'specification', 'number', 'seed', 'number', 'fit', 'pick', 'guess', 'picking', 'curve', 'parameter', 'guess', 'quantity', 'solution', 'value')
originates	('tails',)
tails	('originates', 'statistical')
threshold	('tail', 'percolation', 'polyomino')
tail	('threshold', 'descriptive', 'distribution', 'left', 'small', 'right', 'right', 'large', 'occur', 'occur', 'number', 'length', 'probability', 'probability', 'balanced', 'set', 'test', 'probability', 'event', 'probability', 'probability', 'probability', 'probability', 'distribution', 'occur', 'expected', 'number', 'approach', 'kuiper', 'coin', 'probability', 'distribution', 'rimmer')
head	('statistic', 'skewness', 'only', 'probability', 'player', 'th', 'turn', 'turn', 'turn', 'minus', 'probability', 'beautiful', 'smallest', 'expected', 'minus')
equivalent	('three', 'markov', 'papoulis', 'parameter', 'square', 'version', 'though', 'one', 'cluster-based', 'take', 'trial', 'repeated', 'typically', 'case', 'continuous')
u	('statistic',)
encountering	('probability', 'th')
roughly	('word', 'up', 'keller', 'lie', 'line', 'usage', 'synonymous', 'follow', 'normal')
breaks	('law', 'down')
frequent	('less', 'most', 'permutation')
harmonic	('word', 'statistic', 'series', 'mean', 'value', 'mean', 'mean', 'arithmetic', 'mean', 'mean', 'mean', 'mean', 'geometric', 'confidence', 'spherical', 'year', 'mean', 'index', 'mean', 'index', 'mean', 'constant', 'generalized')
diverges	('pierce',)
pierce	('diverges',)
statement	('p', 'malkevitch', 'shephard', 'refers', 'hypothesis')
incorrect	('goetz',)
goetz	('incorrect', 'law')
inversely	('word', 'proportional')
proportional	('inversely', 'statistical', 'length', 'total', 'distribution')
zipf	('word', 'law', 'rank', 'distribution', 'distribution', 'test', 'law', 'distribution', 'distribution', 'number', 'distribution', 'equation', 'distribution', 'distribution', 'law')
inferred	('measured', 'value', 'measured', 'value', 'information', 'limited')
sum	('absolute', 'relative', 'example', 'should', 'th', 'example', 'example', 'relations', 'value', 'equal', 'value', 'distribution', 'field', 'elements', 'variance', 'two', 'minimizing', 'square', 'residuals', 'absolute', 'relationship', 'linear', 'similar', 'test', 'weighted', 'several', 'weights', 'unity', 'gave', 'expression', 'distribution', 'discrete', 'function', 'distribution', 'distribution', 'probabilities', 'exponential', 'step', 'done', 'even', 'evaluated', 'odd', 'evaluated', 'plane', 'two-dimensional', 'rank', 'test', 'first', 'squared', 'value', 'squared', 'error', 'squared', 'minimizing', 'curve', 'vertical', 'finding', 'unsquared', 'value', 'square', 'minimize', 'square', 'residual', 'variance', 'expanded', 'fact', 'those', 'charlier', 'level', 'square', 'total', 'multivariate', 'using', 'probabilities', 'computed', 'example', 'indeed', 'required', 'less', 'rank', 'test', 'cumulative', 'exponential', 'width', 'jacobian', 'distribution', 'gaussian', 'distribution', 'normal', 'distribution', 'variable', 'large', 'normal', 'distribution', 'normal', 'normal', 'distribution', 'normal', 'distribution', 'normal', 'distribution', 'distribution', 'two', 'hold', 'normally', 'weighted', 'independent', 'random', 'normal', 'distribution', 'uniform', 'distribution', 'uniform', 'distribution', 'uniform', 'distribution', 'uniform', 'distribution', 'distribution', 'uniform', 'distribution', 'exceeds', 'probability', 'greater', 'number', 'first', 'number', 'first', 'uniform', 'distribution', 'separately', 'computed', 'normalized', 'probabilities', 'distribution', 'distribution', 'term', 'asymptotically', 'random', 'consisting', 's', 'compared', 'sense')
propagation	('error', 'percentage', 'error', 'precision', 'error', 'error', 'error', 'percent', 'error', 'fixed', 'error', 'percentage', 'track', 'error', 'fixed', 'error', 'mean')
percentage	('propagation', 'error', 'error', 'error', 'covariance', 'error', 'minus', 'error', 'error', 'error', 'error', 'error', 'propagation', 'error', 'analysis', 'categories', 'increase', 'difference')
correct	('quantity', 'free', 'verify', 'obtain', 'error', 'solution', 'argument', 'combining', 'probability', 'probabilities')
free	('correct', 'two', 'number', 'two', 'two', 'four', 'distribution')
accuracy	('absolute', 'meaning', 'relative', 'meaning', 'concepts', 'confused', 'number', 'number', 'digit', 'error', 'error', 'covariance', 'precision', 'number', 'number', 'error', 'arbitrary', 'numerical', 'analysis', 'arithmetic', 'analysis', 'fractional', 'measure', 'sample')
concepts	('range', 'accuracy', 'computation')
precision	('closely', 'total', 'propagation', 'relative', 'calculation', 'arbitrary', 'computation', 'arbitrary', 'error', 'fixed', 'fixed', 'significance', 'error', 'relative', 'accuracy', 'closely', 'point', 'total', 'fixed', 'error', 'arbitrary', 'error', 'fixed', 'relative', 'information', 'most', 'fixed', 'fixed', 'significant', 'function', 'rounding')
confused	('accuracy', 'should', 'correlation')
significant	('number', 'decimal', 'number', 'decimal', 'error', 'error', 'number', 'decimal', 'number', 'decimal', 'arithmetic', 'precision', 'number', 'digit', 'figure', 'number', 'number', 'number', 'number', 'smallest', 'figure', 'quantity', 'only', 'only', 'least', 'bit', 'doing', 'amount', 'statistically', 'association', 'least', 'one', 'null', 'other', 'under')
roundoff	('error', 'error')
computer	('most', 'programs', 'largest', 'digit', 'programs')
programs	('computer', 'computing', 'computer', 'written')
calculation	('precision', 'even', 'using')
addition	('limited', 'machine', 'two', 'uncorrelated', 'quantities', 'property', 'opposite', 'use', 'set', 'fitting', 'minimizing', 'tukey', 'probability', 'random', 'renyi', 'chebyshev')
limited	('addition', 'word', 'inferred', 'number', 'parameter', 'domain')
stored	('number', 'one', 'need')
processor	('one', 'common', 'word')
mid-2002	('most',)
bits	('integer', 'get', 'one', 'get', 'most')
general	('integer', 'integer', 'unbiased', 'mean', 'behavior', 'correlation', 'no', 'probability', 'computed', 'set', 'subset', 'racs', 'setting', 'exist', 'computation', 'polyhedron', 'specify', 'net', 'topology', 'distribution', 'certain', 'time-dependent', 'time', 'ponitz', 'most', 'case', 'type', 'variable', 'case', 'correlation', 'probability', 'predicate', 'mathematical', 'type', 'angle', 'cauchy', 'zero', 'distribution', 'fischer', 'distribution', 'distribution', 'type', 'distribution', 'case', 'distribution', 'normal', 'variance', 'distribution', 'writing', 'recurrence', 'a086117', 'case', 'function', 'distribution', 'function', 'bound', 'function', 'distribution', 'memoryless', 'platykurtic', 'range', 'distribution', 'constant', 'theorem', 'distribution', 'distribution', 'surrogate', 'function', 'distribution', 'distribution')
arithmetic	('integer', 'machine', 'arbitrary-precision', 'set', 'arbitrary-precision', 'knowing', 'significance', 'significance', 'significant', 'significance', 'approximate', 'significance', 'extremely', 'high-end', 'significance', 'error', 'accuracy', 'error', 'significance', 'truncate', 'moment', 'mean', 'mean', 'mean', 'value', 'moment', 'mean', 'mean', 'geometric', 'moment', 'mean', 'mean', 'moment', 'geometric', 'mean', 'harmonic', 'plot', 'mean', 'plot', 'mean', 'significance', 'significance', 'sequence', 'anova', 'mean', 'theorem', 'strong', 'theorem', 'law', 'theorem', 'law')
machine	('arithmetic', 'addition', 'create', 'language', 'bean', 'discrete', 'device')
get	('number', 'bits', 'number', 'bits', 'people', 'chance', 'tosses', 'subsequences', 'naturally', 'higher-dimensional')
overflow	('plus',)
bit	('multiplication', 'significant', 'nearest', 'distribution', 'work', 'second', 'fair')
prevalent	('most', 'programming')
programming	('prevalent', 'many')
access	('cannot', 'higher')
programmer	('depend', 'either')
create	('either', 'machine', 'side', 'square', 'tukey', 'box-and-whisker')
slower	('function', 'function')
c	('function', 'final')
final	('c', 'overhead', 'amount', 'payoff', 'residual', 'digit', 'variance', 'computed')
overhead	('final', 'nine')
nine	('overhead', 'multiplies', 'angle', 'correlated')
multiplies	('nine', 'division')
division	('multiplies', 'number', 'number', 'error', 'quantities', 'two')
creating	('number', 'quotient', 'difficulty', 'arbitrary-precision')
quotient	('creating', 'arbitrary-precision')
arbitrary-precision	('quotient', 'arithmetic', 'creating', 'arithmetic')
structures	('data', 'designed')
designed	('structures', 'specifically')
specifically	('designed', 'deal', 'value', 'uspensky')
deal	('specifically', 'great', 'random')
arbitrary	('number', 'built', 'precision', 'number', 'precision', 'accuracy', 'precision', 'start', 'person', 'assumed', 'real', 'unity', 'taken', 'angle', 'curve', 'out', 'minimum', 'distribution', 'normal', 'distribution', 'covariance', 'function', 'probability', 'average')
modify	('function', 'standard')
paper-and-pencil	('standard', 'arithmetical')
arithmetical	('paper-and-pencil', 'techniques')
techniques	('arithmetical', 'long')
long	('techniques', '◇', 'inverted', 'a060294', 'needle', 'ahead', 'newton', 'letter', 'payoff', 'run', 'increasing', 'processes', 'arbitrarily', 'string')
broken	('number', 'word-size')
word-size	('broken',)
chunks	('major',)
difficulty	('major', 'creating')
stop	('knowing', 'always', 'gets', 'tend', 'rotating')
simple	('computation', 'example', 'papoulis', 'random', 'case', 'set', 'function', 'non-explosive', 'point', ';', 'point', 'very', 'surprisingly', 'nature', 'space', 'point', 'process', 'point', 'particularly', 'continued', 'process', 'point', 'process', 'point', 'process', 'point', 'point', 'jacobsen', 'point', 'process', 'point', 'process', 'point', 'originally', 'temporal', 'process', 'point', 'seed', 'generator', 'fold', 'symmetrical', 'method', 'elegant', 'site', 'symmetric', 'type', 'inclusively', 'code', 'displaying', 'statistical', 'identity', 'approximation')
binary	('problem', 'expansion', 'nonterminating', 'decimal', 'terminating', 'fraction', 'processes', 'interpreting', 'reversing', 'coordinate', 'representing', 'interpreting', 'fraction')
expansion	('binary', 'nonterminating', 'asymptotic', 'difference', 'asymptotic', 'gamma', 'formal', 'hermite', 'cornish', 'asymptotic', 'edgeworth', 'asymptotic', 'statistical', 'charlier', 'bernoulli', 'asymptotic', 'characteristic', 'function', 'wallace', 'term', 'cramer', 'charlier', 'asymptotic', 'poisson', 'term', 'treating', 'series', 'probability', 'series', 'integrand')
nonterminating	('expansion', 'binary')
exact	('fact', 'approximation', 'correlation', 'theorem', 'relationship', 'sample', 'test', 'fisher', 'test', 'developed', 'fisher', 'test', 'fisher', 'test', 'no', 'expression')
terminating	('number', 'binary')
expansions	('additional',)
additional	('expansions', 'functionality', 'heard', 'qualification', 'use', 'column', 'amount', 'machinery', 'multiplied', 'factor', 'tukey', 'variation', 'under')
functionality	('additional', 'built')
built	('functionality', 'arbitrary')
system	('either', 'seed', 'product', 'hilbert', 'bounded', 'space', 'bounded', 'space', 'satisfy', 'underlying', 'normal', 'pearson', 'ratio', 'equation', 'pearson', 'continuous', 'involving')
failsafe	('configurable',)
configurable	('failsafe', "'maximum")
'maximum	('configurable', "precision'")
precision'	("'maximum", 'computation')
always	('computation', 'stop', 'remaining', 'approximately', 'variable', 'casinos', 'come', 'variable', 'round', 'somewhat', 'model', 'produce', 'almost', 'minimized', 'almost', 'minimized', 'quantity', 'almost', 'clump', 'statistic')
gets	('stop', 'particular')
very	('particular', 'small', 'model', 'loosely', 'only', 'simple', 'event', 'important', 'distribution', 'close', 'strangely', 'difficult', 'converge', 'well', 'become', 'variable')
fixed	('analysis', 'precision', 'precision', 'quantity', 'error', 'number', 'done', 'precision', 'propagation', 'precision', 'over', 'propagation', 'precision', 'precision', 'pays', 'amount', 'trial', 'number', 'certain', 'only', 'number', 'line', 'point', 'performance', 'number', 'trial', 'probability', 'distribution', 'even', 'size', 'equation')
significance	('precision', 'arithmetic', 'value', 'standard', 'error', 'arithmetic', 'arithmetic', 'uncertainty', 'arithmetic', 'language', 'arithmetic', 'rounding', 'arithmetic', 'random', 'testing', 'value', 'distribution', 'test', 'acceptable', 'value', 'increase', 'interval', 'level', 'recommended', 'statistical', 'error', 'arithmetic', 'arithmetic', 'test', 'chance', 'test', 'test', 'statistical', 'value', 'sensitivity', 'test', 'distribution', 'standard')
trial	('measurement', 'above', 'tosses', 'relevant', 'problem', 'bernoulli', 'cards', 'coincidence', 'space', 'nothing', 'fixed', 'outputs', 'same', 'lie', 'deterministic', 'equivalent', 'probability', 'differ', 'poisson', 'bernoulli', 'bernoulli', 'bernoulli', 'experiment', 'outcome', 'event', 'space', 'event', 'ghost', 'bernoulli', 'bernoulli', 'lexis', 'subnormal', 'probability', 'bernoulli', 'bernoulli', 'lexis', 'event', 'experiment', 'probability', 'success', 'number', 'poisson', 'poisson', 'experiment', 'population', 'sampling', 'sample', 'sample', 'quantile', 'nyquist', 'subnormal', 'lexis', 'lexis', 'supernormal', 'bernoulli', 'bernoulli', 'lexis', 'subnormal', 'statistic', 'single', 'bottom', 'bernoulli', 'bernoulli', 'event', 'outcome', 'fixed', 'success', 'bernoulli', 'distribution', 'curtailed', 'geometric', 'estimator', 'expectation', 'bernoulli', 'binomial', 'probability', 'bernoulli', 'true', 'binomial', 'bernoulli', 'consisting', 'fraction', 'success', 'probability', 'limit', 'probability', 'value', 'function', 'random')
interest	('interval', 'symmetrically')
symmetrically	('interest', 'placed', 'probability', 'placed')
placed	('symmetrically', 'around', 'column', 'row', 'symmetrically')
conversely	('find', 'univariate')
probability-	('confidence', 'confidence')
centered	('interval', 'mean', 'named', 'fall')
equation	('solve', 'obtain', 'wald', 'wald', 'expectation', 'wald', 'transitional', 'kolmogorov', 'markov', 'markov', 'kolmogorov', 'markov', 'recurrence', 'working', 'deriving', 'hand', 'already', 'expand', 'obtain', 'expressed', 'whereby', 'solving', 'ceiling', 'form', 'kostlan', 'form', 'form', 'take', 'notice', 'reduces', 'differential', 'form', 'differential', 'analogue', 'heisenberg', 'quantum', 'notation', 'polynomial', 'solved', 'reproduces', 'solution', 'desire', 'obtain', 'pick', 'solved', 'problem', 'proceed', 'normal', 'normal', 'normal', 'because', 'normal', 'regression', 'normal', 'projection', 'value', 'above', 'written', 'expression', 'connecting', 'distribution', 'logistic', 'lorentzian', 'switches', 'differential', 'normal', 'solution', 'been', 'system', 'differential', 'normal', 'fixed', 'transcendental', 'cannot', 'above', 'zipf', 'p', 'central')
inverse	('obtain', 'erf', 'erf', 'distribution', 'error', 'erf', 'using', 'binomial', 'kenney', 'matrix', 'moore', 'matrix', 'nonlinear', 'particular', 'matrix', 'regression', 'drazin', 'matrix', 'matrix', 'moore', 'matrix', 'unique', 'matrix', 'moore-penrose', 'satisfies', 'problem', 'matrix', 'regression', 'drazin', 'least', 'matrix', 'matrix', 'matrix', 'nonlinear', 'object', 'special', 'matrix', 'matrix', 'matrix', 'moore', 'matrix', 'normal', 'function', 'fourier', 'distribution', 'chi', 'distribution', 'gumbel', 'gaussian', 'parameter', 'gaussian', 'excess', 'gaussian', 'distribution', 'gaussian', 'function', 'fourier', 'p', 'distribution', 'erf', 'p', 'distribution', 'gaussian', 'distributed', 'function', 'theorem', 'fourier')
representative	('interval', 'small')
returned	('value',)
normalci	('confidencelevel',)
confidencelevel	('normalci',)
package	('language', 'application', 'application', 'application', 'application', 'application', 'application', 'application', 'application', 'application', 'loading', 'loading', 'application', 'application', 'application', 'language', 'language', 'language', 'language', 'language', 'language', 'language', 'language', 'language')
hypothesistesting`	('confidence',)
alpha	('limit', 'value', 'probability', 'value', 'value', 'p-value', 'value', 'simultaneously', 'positive', 'set', 'equal', 'test', 'value', 'value', 'test', 'value', 'chance', 'different', 'test', 'value', 'test', 'value', 'level', 'positive', 'th')
erf	('value', 'inverse', 'inverse', 'normal', 'inverse', 'standard', 'complementary', 'function', 'spiegel', 'function', 'expressed', 'error', 'theorem', 'error', 'function', 'expressed', 'oeis', 'oeis', 'interval', 'inverse', 'normal', 'distribution', 'normal')
endpoints	('confidence',)
remaining	('error', 'always', 'interval', 'quantities')
last	('approximately', 'term', 'only', 'sample', 'believed', 'case', 'beginning', 'virtually', 'removing')
dropped	('equiripple', 'ball', 'funnel', 'opening', 'kozlov', 'completely', 'out')
equiripple	('dropped', 'error')
chebyshev	('analysis', 'polynomial', 'approximated', 'case', 'charlier', 'addition', 'theorem', 'inequality')
polynomial	('chebyshev', 'first', 'minimax', 'minimax', 'multivariate', 'multivariate', 'multivariate', 'univariate', 'variate', 'degree', 'random', 'complementary', 'fitting', 'least', 'lead', 'th', 'residual', 'equation', 'fit', 'fitting', 'regression', 'fitting', 'multiple', 'smallest', 'first', 'minimax', 'regression', 'above', 'oeis', 'a-series', 'cornish', 'form', 'degree', 'wolfram', 'stirling')
kind	('first', 'elliptic', 'processes', 'originally', 'jacobi', 'numerical', 'minimax', 'raw', 'first', 'first', 'distribution', 'distribution', 'following', 'sample', 'order', 'dobiński')
elliptic	('kind', 'rational', 'complete', 'integral', 'complete', 'integral', 'regression', 'rational')
rational	('elliptic', 'function', 'fraction', 'number', 'elliptic', 'function')
margin	('error', 'error', 'error', 'poll', 'error', 'size', 'error', 'function', 'error', 'error')
uncorrelated	('addition', 'explicitly', 'converse', 'converse', 'theorem', 'uniformly', 'random', 'legendre', 'formula', 'case', 'variable', 'converse', 'true', 'time', 'statistic', 'number', 'satisfies', 'satisfies', 'sequence', 'analysis')
rearranging	('through', 'exponentiation', 'function', 'normal', 'integral', 'bring', 'generalized', 'solving')
exponentiation	('rearranging', 'quantities')
covariance	('accuracy', 'percentage', 'variate', 'two', 'variate', 'correlated', 'case', 'reduces', 'correlation', 'useful', 'variate', 'symmetric', 'denoted', 'quantities', 'matrix', 'induction', 'coefficient', 'matrix', 'linear', 'using', 'check', 'check', 'matrix', 'probability', 'matrix', 'vector', 'vector', 'describing', 'two', 'two', 'linear', 'ratio', 'least', 'two', 'element', 'regression', 'regression', 'matrix', 'coefficient', 'difference', 'independent', 'analysis', 'independent', 'unit', 'matrix', 'matrix', 'arbitrary', 'distribution', 'bivariate', 'probability', 'summation', 'multinomial')
educated	('estimate', 'guess', 'allowing', 'guesses')
guess	('educated', 'unknown', 'initial', 'obtain', 'dotted', 'initial', 'converged')
unknown	('guess', 'quantity', 'model', 'function', 'population', 'number', 'linear', 'three', 'universe', 'mean', 'universe', 'mean', 'variate')
outcome	('quantity', 'based', 'house', 'concept', 'likelihood', 'first', 'highest', 'conventional', 'possible', 'within', 'axiom', 'probability', 'probability', 'probability', 'first', 'probabilities', 'event', 'trial', 'event', 'probability', 'subset', 'uniquely', 'pp', 'lead', 'cannot', 'trial', 'poisson', 'labelled', 'distribution', 'dependent', 'depend', 'possible', 'occur', 'lindeberg')
making	('information', 'resolved', 'distinction', 'test', 'use', 'distribution', 'substitution')
care	('statistic', 'provide', 'extreme', 'should', 'moment', 'interpreting', 'extreme', 'should', 'though', 'should', 'distribution', 'obtain')
provide	('care', 'accurate', 'measure', 'consistent', 'measure', 'alone', 'adequate', 'random', 'fitting', 'simpler', 'solution', 'fitting', 'simpler')
accurate	('provide', 'estimate', 'one', 'least', 'obtain')
little	('using', 'input', 'many', 'problem')
input	('little', 'data', 'frequently', 'simulation')
uncertainty	('estimate', 'estimate', 'significance', 'within')
rule	('statistically', 'tells', 'estimator', 'tells', 'automaton', 'central')
tells	('rule', 'calculate', 'rule', 'calculate', 'observation', 'us')
contained	('measurement', 'sample', 'measurement', 'derivation', 'needle', 'entirely', 'actually', 'error')
bias	('estimator', 'estimator', 'estimator', 'estimator', 'expectation', 'estimator', 'estimator', 'turns')
frequently	('measurement', 'cited', 'statistic', 'encountered', 'less', 'encountered', 'variate', 'input', 'unfortunate')
cited	('frequently', 'theory', 'one')
poll	('phrase', 'margin')
minus	('plus', 'percentage', 'head', 'head')
heard	('additional',)
qualification	('additional', 'percent', 'word')
percent	('qualification', 'confidence', 'propagation', 'relative')
indicate	('precisely', 'what', 'p', 'particular', 'subscript', 'reference', 'model', 'problem', 'expectation')
minimax	('term', 'approximation', 'algorithm', 'polynomial', 'polynomial', 'theorem', 'kind', 'polynomial', 'function', 'approximation')
approximation	('minimax', 'error', 'variable', 'exact', 'function', 'number', 'poorer', 'diaconis', 'suffice', 'minimum', 'tosses', 'bernoulli', 'stochastic', 'stochastic', 'minimax', 'distribution', 'binomial', 'assumption', 'due', 'value', 'maclaurin', 'value', 'asymptotic', 'simple', 'two', 'functional', 'due', 'value', 'table', 'binomial', 'find')
remez	('analysis', 'algorithm')
algorithm	('remez', 'minimax', 'classes', 'search', 'based', 'shuffling', 'class', 'analyzed', 'schrage', 'stochastic', 'dynamical')
product	('number', 'function', 'distribution', 'complex', 'system', 'dow', 'several', 'outer', 'obtain', 'outer', 'taken', 'gaussian', 'distribution', 'normal', 'distribution', 'variable', 'large', 'normal', 'distribution', 'distribution', 'two', 'expression', 'three', 'normal', 'distribution', 'normal', 'distribution', 'normal', 'distribution', 'uniform', 'distribution', 'uniform', 'distribution', 'distribution', 'uniform', 'uniform', 'distribution', 'uniform', 'distribution', 'uniform', 'distribution', 'variable', 'distribution', 'distribution')
keeps	('only', 'track')
track	('keeps', 'numerical', 'propagation', 'regions', 'movements')
carry	('computation',)
returning	('information', 'end')
end	('returning', 'numerical', 'small', 'large', 'paradox', 'start', 'composed', 'range', 'many')
together	('quantity', 'estimated', 'event', "outcomes'", 'taken', 'comprise', 'variety')
extremely	('arithmetic', 'powerful', 'amount', 'flexible', 'event', 'unlikely', 'play', 'important', 'sequence', 'useful')
powerful	('extremely', 'technique')
technique	('powerful', 'offers', 'estimation', 'insensitive', 'rely', 'analysis', 'classification', 'tibshirani', 'estimation', 'nonparametric', 'describing', 'artificial', 'estimation', 'based', 'müller', 'regression', 'fitting', 'easily', 'fitting', 'simplest', 'gaussian', 'matrix', 'could', 'analogous', 'solve', 'behind', 'observation', 'population', 'analogous')
offers	('technique', 'many')
advantages	('many', 'over')
floating-point	('integer',)
high-end	('arithmetic', 'mathematical')
mathematical	('high-end', 'software', 'encountered', 'naturally', 'lacking', 'rigor', 'higher', 'skills', 'established', 'study', 'walk', 'properties', 'mathematics', 'procedure', 'general', 'p', 'object')
software	('mathematical',)
scientific	('expressed',)
notation	('number', 'use', 'rose', 'mean', 'uninformative', 'unbiased', 'normalized', 'mean', 'macron', 'expectation', 'value', 'mean', 'optimal', 'first', 'skewness', 'unfortunately', 'moment', 'due', 'kenney', 'uninformative', 'bias-corrected', 'daley', 'expanded', 'log-likelihood', 'phase', 'equation', 'central', 'usual', 'due')
express	('digit', 'number')
subtraction	('number',)
should	('sum', 'written', 'care', 'exercised', 'care', 'exercised', 'why', 'he', 'care', 'exhibited', 'residual', 'confused', 'test', 'produce')
written	('should', 'variance', 'second', 'mean', 'out', 'variance', 'population', '◇', 'solving', 'event', 'papoulis', 'explicitly', 'odd', 'form', 'set', 'denotes', 'fukuda', 'routines', 'programs', 'solution', 'square', 'reduce', 'component', 'formula', 'distribution', 'half', 'equation', 'probability', 'word', 'sentences', 'recurrence', 'special', 'parameter', 'pearson', 'interval', 'function', 'distribution', 'distribution', 'excess', 'first')
truncate	('arithmetic',)
exhibits	('estimator', 'estimator')
biased	('estimator', 'estimator', 'estimator', 'estimator', 'estimator', 'estimator', 'deviation', 'estimator', 'estimator', 'estimator', 'estimator', 'reason')
square	('mean', 'error', 'matrix', 'mean', 'sample', 'sum', 'residuals', 'variance', 'mean', 'displacement', 'mean', 'displacement', 'mean', 'displacement', 'mean', 'mean', 'deviation', 'mean', 'mean', 'displacement', 'distribution', 'mean', 'root', 'ambiguous', 'root', 'deviation', 'mean', 'standard', 'estimate', 'root', 'equivalent', 'root', 'list', 'root', 'inner', 'fitting', 'grid', 'diameter', 'problem', 'figure', 'side', 'insetting', 'insetting', 'side', 'namely', 'reduces', 'case', 'unit', 'two-dimensional', 'grid', 'two-dimensional', 'grid', 'mean', 'displacement', 'residual', 'correlation', 'fitting', 'offsets', 'offsets', 'offsets', 'fitting', 'fitting', 'fitting', 'fitting', 'analytically', 'written', 'regression', 'fitting', 'fitting', 'fitting', 'fitting', 'fitting', 'fitting', 'fitting', 'fitting', 'fitting', 'fitting', 'fitting', 'fitting', 'fitting', 'fitting', 'fitting', 'perpendicular', 'fitting', 'fitting', 'fit', 'fitting', 'fitting', 'fitting', 'fitting', 'fitting', 'fitting', 'fitting', 'fitting', 'fitting', 'fitting', 'fitting', 'solution', 'create', 'fitting', 'fitting', 'fitting', 'sum', 'fit', 'fitting', 'fitting', 'sum', 'fitting', 'fitting', 'complex', 'fitting', 'fitting', 'fitting', 'sum', 'mean', 'fitting', 'fitting', 'followed', 'root', 'containing', 'independent')
polyache	('value', 'polykay', 'moment', 'computed', 'mathstatica', 'moment')
polykay	('polyache', 'sample', 'distribution', 'sample', 'moment', 'computed', 'mathstatica')
moment	('central', 'sample', 'central', 'estimator', 'mean', 'raw', 'raw', 'wald', 'distribution', 'central', 'central', 'polyache', 'kenney', 'cumulant', 'mean', 'normal', 'central', 'skewness', 'polykay', 'polyache', 'central', 'sample', 'sample', 'power', 'expectation', 'sample', 'central', 'central', 'central', 'raw', 'raw', 'sample', 'sample', 'raw', 'sample', 'arithmetic', 'central', 'sample', 'raw', 'sample', 'sample', 'expected', 'sample', 'sample', 'central', 'sample', 'deviation', 'absolute', 'probability', 'absolute', 'central', 'central', 'central', 'raw', 'raw', 'absolute', 'central', 'bessel', 'univariate', 'expressed', 'those', 'expressed', 'transformations', 'expressed', 'central', 'multivariate', 'expressed', 'central', 'absolute', 'absolute', 'cumulant', 'kurtosis', 'raw', 'raw', 'sample', 'central', 'skewness', 'abramowitz', 'characteristic', 'finite', 'cumulant', 'bracket', 'bracket', 'generating', 'variance', 'bivariate', 'transformations', 'central', 'using', 'characteristic', 'mean', 'sheppard', 'cumulant', 'cumulant', 'generating', 'cage', 'factorial', 'factorial', 'kurtosis', 'homoscedastic', 'heteroscedastic', 'central', 'kurtosis', 'raw', 'central', 'central', 'excess', 'l', 'l', 'order', 'kurtosis', 'taken', 'arithmetic', 'central', 'function', 'absolute', 'raw', 'denoted', 'taken', 'characteristic', 'most', 'denoted', 'second', 'computed', 'function', 'absolute', 'absolute', 'characteristic', 'factorial', 'kurtosis', 'mean', 'generating', 'function', 'problem', 'problem', 'sequence', 'standardized', 'variance', 'independent', 'simpler', 'function', 'generating', 'characteristic', 'function', 'problem', 'problem', 'sequence', 'sequence', 'sequence', 'problem', 'problem', 'problem', 'sequence', 'sequence', 'sequence', 'interval', 'sequence', 'sequence', 'sequence', 'problem', 'skewness', 'kenney', 'bowley', 'bowley', 'expectation', 'arithmetic', 'probability', 'expressed', 'those', 'expressed', 'raw', 'multivariate', 'expressed', 'raw', 'absolute', 'absolute', 'central', 'central', 'mean', 'mean', 'sample', 'raw', 'absolute', 'root', 'arithmetic', 'raw', 'sample', 'sample', 'unbiased', 'rose', 'raw', 'power', 'raw', 'central', 'central', 'raw', 'raw', 'sample', 'sample', 'central', 'sample', 'denotes', 'sample', 'sample', 'sample', 'mean', 'normally', 'corrected', 'class', 'bin', 'notation', 'bowley', 'denotes', 'central', 'natural', 'most', 'central', 'central', 'confidence', 'deviation', 'normal', 'variance', 'sample', 'estimator', 'standardized', 'kurtosis', 'kurtosis', 'skewness', 'care', 'central', 'central', 'charlier', 'mean', 'raw', 'raw', 'sample', 'mean', 'student', 'distribution', 'th', 'bounded', 'distribution', 'other', 'sample', 'sample', 'central', 'sample', 'raw', 'sample', 'papoulis', 'hypergeometric', 'distribution', 'johnson', 'distribution', 'confluent', 'first', 'incomplete', 'raw', 'computed', 'euler-mascheroni', 'papoulis', 'distribution', 'pochhammer', 'first', 'gamma', 'first', 'modified', 'first', 'binomial', 'computed', 'central', 'second', 'first', 'analytically', 'noncentral', 'analytically', 'singly', 'first', 'computed', 'papoulis', 'raw', 'first', 'gamma', 'th', 'th', 'combining', 'combining', 'apery', 'exist', 'gamma', 'first', 'central', 'differentiating', 'analytically', 'analytically', 'distribution', 'central', 'analytically', 'analytically', 'two', 'pochhammer', 'computed', 'computed', 'statistical')
satisfies	('value', 'multiple', 'value', 'excess', 'leptokurtic', 'number', 'term', 'function', 'differentiable', 'zhao', 'property', 'probability', 'case', 'function', 'constrained', 'motion', 'law', 'inverse', 'conjugate', 'run', 'mean', 'term', 'uspensky', 'term', 'uspensky', 'uncorrelated', 'uncorrelated', 'ratio', 'distribution', 'one', 'variable', 'price', 'function', 'frechet', 'function', 'two', 'distribution', 'only', 'overlapping!', 'mean')
multiple	('satisfies', 'discrete', 'variable', 'continuous', 'expectation', 'standard', 'transformation', 'back', 'original', 'line', 'correlation', 'polynomial', 'regression', 'variable', 'regression', 'regression', 'generalized', 'function', 'regression', 'compared', 'response', 'correction', 'iff', 'distribution')
wald	('moment', 'equation', 'random', 'equation', 'value', 'blackwell', 'wolfowitz', 'equation', 'distribution', 'distribution', 'distribution')
compared	('minimum', 'other', 'minimum', 'other', 'preferentially', 'event', 'group', 'multiple', 'small', 'sum')
halmos	('estimator', 'rose', 'estimator', 'rose')
rose	('halmos', 'smith', 'p', 'smith', 'halmos', 'smith', 'notation', 'smith', 'fisher', 'smith', 'introduced', 'smith', 'tukey', 'smith', 'moment', 'smith', 'p', 'smith', 'analytically', 'smith', 'ord', 'smith', 'analytically', 'smith', 'ord', 'smith', 'function', 'smith', 'region', 'smith')
smith	('rose', 'rose', 'rose', 'rose', 'prefer', 'rose', 'rose', 'rose', 'dependence', 'markov', 'rose', 'sample', 'rose', 'rose', 'stuart', 'rose', 'rose', 'stuart', 'rose', 'rose', 'gonick', 'gonick', 'rose')
power	('term', 'data', 'term', 'term', 'moment', 'appearing', 'skewness', 'mean', 'case', 'displacement', 'mean', 'moment', 'equal', 'statistical', 'statistical', 'fitting', 'law', 'fitting', 'law', 'fitting', 'law', 'fitting', 'law', 'interpreted', 'statistical', 'statistical', 'statistical', 'statistical', 'identical', 'noise', 'distribution', 'spectrum')
respectively	('wolfram', 'central', 'matrix', 'rendered', 'altogether', 'jacobsen', 'concept', 'exponential', 'within', 'index', 'form', 'total', 'delta', 'distribution', 'adding', 'joint', 'variance', 'normal')
mathstatica	('h', 'sample', 'polyache', 'polykay', 'central', 'central', 'raw', 'raw', 'sample')
cumulant	('statistical', 'moment', 'kurtosis', 'first', 'moment', 'kurtosis', 'characteristic', 'moment', 'iverson', 'abramowitz', 'expressed', 'estimator', 'function', 'generating', 'function', 'generating', 'function', 'function', 'generating', 'moment', 'moment', 'standard', 'univariate', 'begin', 'check', 'generating', 'function', 'function', 'generating', 'exponentiating', 'ungrouped', 'grouped', 'under', 'standard', 'take', 'via', 'first', 'error', 'subsequent', 'recurrence', 'geometric', 'recurrence', 'subsequent', 'recurrence')
authors	('most', 'kenney', 'variance', 'zwillinger', 'similarly', 'merhdad', 'hawkes', 'processes', 'other', 'two', 'several', 'merhdad', 'case', 'distinguish', 'other', 'completely', 'other', 'function', 'several', 'crudely', 'stationarity', 'use', 'hand', 'view', '**', 'use', 'distribution', 'beyer')
mathematica	('application', 'application', 'application', 'application', 'application', 'application', 'application', 'application', 'application', 'application', 'application')
special	('kenney', 'case', 'function', 'case', 'true', 'case', 'root-mean-square', 'case', 'probability', 'case', 'probability', 'case', 'denoted', 'tile', 'processes', 'case', 'condition', 'processes', 'case', 'certain', 'classes', 'inverse', 'case', 'a050233', 'case', 't', 'distribution', 'case', 'interval', 'case', 'case', 'case', 'distribution', 'case', 'written', 'distribution', 'deviation', 'case')
parent	('normal', 'underlying')
church	('excess',)
carver	('p', 'irwin')
irwin	('carver', 'kendall')
kendall	('irwin', 'kenney', 'identities', 'operator', 'see', 'et', 'variance', 'et')
k	('excess', 'statistic', 'originally', 'unbiased', 'sample')
estimation	('based', 'based', 'point', 'theory', 'based', 'robust', 'technique', 'robust', 'technique', 'sample', 'nonparametric', 'statistical', 'nonparametric', 'no', 'artificial', 'form', 'nonlinear', 'kernel', 'specifies', 'nonparametric', 'statistical', 'technique')
linear	('based', 'l-estimate', 'data', 'transformation', 'covariance', 'sum', 'hawkes', 'processes', 'processes', 'hawkes', 'classical', 'model', 'based', 'fitting', 'regression', 'normalized', 'scheme', 'expressed', 'scale', 'using', 'recurrence', 'seed', 'congruence', 'simplest', 'congruence', 'completion', 'span', 'bounded', 'covariance', 'least', 'coefficient', 'least', 'form', 'formula', 'least', 'parameter', 'least', 'use', 'minimum', 'reproduces', 'regression', 'unknown', 'form', 'regression', 'form', 'regression', 'regression', 'regression', 'regression', 'regression', 'fitting', 'regression', 'regression', 'fitting', 'regression', 'using', 'least', 'similarly', 'future', 'predictability', 'redundancy', 'entropy', 'redundancy', 'variance', 'function', 'uniform')
combinations	('order', 'order', 'order')
l	('trimean', 'estimate', 'estimator', 'estimate', 'estimator', 'estimate', 'estimate', 'estimator', 'estimate', 'estimate', 'population', 'moment', 'moment', 'hinge', 'estimate')
r	('estimate', 'estimate', 'estimate', 'estimate', 'test', 'estimate', 'estimate', 'estimate', 'test', 'estimate', 'distribution', 'estimate')
arguments	('m', 'estimate')
finding	('procedure', 'value', 'procedure', 'best-fitting', 'problem', 'best', 'proceeds', 'sum', 'point', 'minimum', 'problem', 'probability', 'method', 'value')
bernoulli	('denoted', 'md', 'th', 'skewness', 'approximation', 'probability', 'distribution', 'distribution', 'trial', 'jakob', 'ignorant', 'player', 'coin', 'pp', 'form', 'expansion', 'distribution', 'trial', 'trial', 'trial', 'distribution', 'variance', 'trial', 'trial', 'trial', 'trial', 'out', 'variance', 'trial', 'trial', 'trial', 'trial', 'distribution', 'function', 'distribution', 'trial', 'example', 'distribution', 'distribution', 'distribution', 'independent', 'mean', 'population', 'population', 'deviation', 'distribution', 'distribution', 'trial', 'out', 'trial', 'distribution', 'distribution', 'ball', 'trial', 'distribution', 'distribution', 'variate', 'theorem', 'distribution', 'theory')
ahead	('likelihood', 'out', 'long', 'out', 'out', 'cannot')
weighted	('deviation', 'normal', 'expressing', 'sum', 'group', 'inversion', 'macmahon', 'inversion', 'milne', 'inversion', 'point', 'differently', 'exponentially', 'moving', 'form', 'sum', 'variance', 'variable')
poisson	('mean', 'distribution', 'distribution', 'inhomogeneous', 'process', 'inhomogeneous', 'process', 'inhomogeneous', 'process', 'process', 'process', 'process', 'process', 'process', 'hawkes', 'process', 'process', 'motion', 'motion', 'process', 'theorem', 'trial', 'theorem', 'expansion', 'distribution', 'trial', 'trial', 'outcome', 'distribution', 'distribution', 'th', 'event', 'distribution', 'distribution', 'distribution', 'distribution', 'time', 'th', 'event', 'event', 'th', 'event', 'converge', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'value', 'distribution', 'expected', 'distribution', 'probabilities', 'distribution', 'function', 'distribution', 'function', 'distribution', 'deviation', 'distribution', 'distribution', 'distribution', 'function', 'distribution', 'variable', 'parameter', 'distribution', 'generalization', 'distribution', 'indeed', 'distribution', 'similarly', 'distribution', 'distribution', 'process', 'process', 'theorem', 'process', 'process', 'distribution', 'distribution', 'process', 'process', 'distribution')
harris	('maximum', 'stocket', 'parameter', 'stocker')
stocket	('harris',)
generalize	('statistic', 'statistic')
originally	('h', 'tracy', 'k', 'dressel', 'pepys', 'believed', 'racs', 'kind', 'simple', 'object', 'proposed')
tracy	('originally', 'gupta')
gupta	('tracy', 'term')
introduced	('term', 'rose', 'term', 'tukey', 'up', 'coin', 'concept')
computed	('polyache', 'using', 'polykay', 'using', 'mark', 'well', 'quantities', 'moment', 'using', 'mean', 'before', 'defining', 'using', 'distribution', 'student', 'variance', 'sample', 'coefficient', 'original', 'general', 'using', 'sayrafiezadeh', 'explicitly', 'been', 'hernández-navarro', 'edge', 'using', 'number', 'noonan', 'ponitz', 'fit', 'fit', 'least', 'histogram', 'frequency', 'test', 'sum', 'moment', 'defining', 'moment', 'using', 'either', 'numerically', 'function', 'using', 'moment', 'computing', 'either', 'numerically', 'intermediate', 'using', 'messy', 'value', 'direct', 'final', 'sum', 'moment', 'moment', 'region', 'efficiently')
dressel	('originally', 'term')
robust	('test', 'estimation', 'test', 'estimation', 'nonparametric', 'pp')
insensitive	('technique', 'small')
departures	('small', 'idealized')
idealized	('departures', 'assumptions', 'coin', 'obtain')
assumptions	('idealized', 'been')
optimize	('been',)
m-estimates	('follow',)
follow	('m-estimates', 'maximum', 'class', 'two', 'sequence', 'begin', 'time', 'two', 'basic', 'hudson', 'likelihood', 'etc', 'roughly')
r-estimates	('based',)
relations	('sum',)
hat	('indicating',)
indicating	('hat', 'quantity', 'structure')
priori	('elements', 'elements')
zwillinger	('authors', 'prefer', 'p', 'p')
distinction	('variance', 'common', 'sample', 'common', 'making', 'amount', 'depend', 'rise')
source	('common', 'common')
confusion	('extreme', 'extreme')
exercised	('should', 'consulting', 'should', 'consulting')
consulting	('exercised', 'literature', 'exercised', 'literature')
literature	('consulting', 'convention', 'consulting', 'convention', 'univariate', 'intensity', 'variety', 'daley')
uninformative	('use', 'notation', 'use', 'notation')
exhibit	('quantity', 'estimator')
blackwell	('wald', 'wolfowitz')
wolfowitz	('blackwell', 'wald')
transitional	('equation', 'densities', 'pp', 'densities')
densities	('transitional', 'markov', 'transitional', 'markov', 'equal', 'probability')
markov	('densities', 'equation', 'processes', 'processes', 'process', 'chain', 'processes', 'processes', 'chain', 'chain', 'word', 'sequence', 'chain', 'example', 'features', 'chain', 'chain', 'chain', 'processes', 'event', 'sequence', 'process', 'equivalent', 'p', 'process', 'process', 'processes', 'variate', 'densities', 'sequence', 'equation', 'sequence', 'sequence', 'processes', 'equation', 'chain', 'governed', 'smith', 'process', 'theorem', 'processes', 'processes', 'process', 'matrix', 'matrix', 'finite', 'matrix', 'processes', 'majorization', 'chain', 'qed', 'inequality', 'board', 'chain', 'statistic', 'chain', 'following')
papoulis	('integer', 'chapman', 'chain', 'simple', 'equivalent', 'only', 'transform', 'origin', 'function', 'transform', 'written', 'doob', 'process', 'triangle', 'parameter', 'uspensky', 'field', 'experiment', 'satisfy', 'independent', 'ambiguity', 'experiment', 'flipping', 'moment', 'moment', 'form', 'incomplete', 'first', 'moment', 'see', 'distribution', 'time', 'distribution', 'distribution', 'distribution')
chapman	('papoulis', 'kolmogorov', 'processes', 'kolmogorov')
kolmogorov	('chapman', 'equation', 'chapman', 'equation', 'set', 'axioms', 'number', 'weight', 'subset', 'axioms', 'axiom', 'test', 'smirnov', 'test', 'smirnov', 'r-estimate', 'smirnov', 'test', 'smirnov', 'distribution', 'smirnov', 'feller', 'established', 'sequence')
processes	('markov', 'markov', 'markov', 'markov', 'markov', 'conditional', 'markov', 'doob', 'markov', 'chapman', 'markov', 'markov', 'markov', 'doubly', 'hawkes', 'hawkes', 'many', 'summand', 'upon', 'point', 'conditional', 'authors', 'hawkes', 'specified', 'linear', 'linear', 'hawkes', 'differentiated', 'one', 'one', 'inhomogeneous', 'one', 'hawkes', 'liniger', 'hawkes', 'carlsson', 'point', 'point', 'special', 'point', 'occurrence', 'regarded', 'point', 'daley', 'point', 'counting', 'counting', 'random', 'special', 'point', 'spatiotemporal', 'spatio-temporal', 'space-time', 'spatial', 'point', 'kind', 'point', 'binary', 'point', 'long', 'point', 'point', 'merely', 'temporal', 'without', 'boson', 'exponential', 'adapted', 'exponential', 'stochastic', 'operator', 'canonical', 'naturally', 'waiting')
process	('markov', 'random', 'future', 'markov', 'markov', 'markov', 'no', 'markov', 'theorem', 'markov', 'statistical', 'control', 'hawkes', 'conditional', 'rate', 'hawkes', 'other', 'intensity-based', 'temporal', 'point', 'history', 'cluster', 'only', 'poisson', 'rate', 'univariate', 'described', 'adapting', 'different', 'poisson', 'intensity', 'point', 'intensity', 'poisson', 'intensity', 'hawkes', 'excitation', 'immigrant', 'th', 'offspring', 'merhdad', 'hawkes', 'among', 'hawkes', 'whenever', 'hawkes', 'time', 'point', 'poisson', 'poisson', 'probability', 'point', 'stochastic', 'point', 'univariate', 'point', 'temporal', 'point', 'counting', 'time', 'point', 'hawkes', 'hawkes', 'repeat', 'one', 'pennies', 'repeated', 'hawkes', 'point', 'quantity', 'point', 'provided', 'point', 'probability', 'relative', 'point', 'interval', 'point', 'intimately', 'borel', 'point', 'time', 'point', 'stationary', 'point', 'point', 'form', 'point', 'point', 'point', 'point', 'mark', 'point', 'time', 'point', 'self', 'point', 'self', 'point', 'simple', 'point', 'spatial', 'point', 'spatial', 'point', 'temporal', 'point', 'point', 'measurable', 'point', 'abbreviated', 'despite', 'point', 'time', 'point', 'point', 'point', 'random', 'point', 'probabilistic', 'poisson', 'point', 'time', 'point', 'poisson', 'poisson', 'self', 'point', 'self', 'point', 'simple', 'point', 'spatial', 'point', 'spatial', 'point', 'temporal', 'point', 'point', 'point', 'point', 'self-correcting', 'intuitively', 'self-correcting', 'point', 'time', 'point', 'point', 'point', 'self', 'point', 'simple', 'point', 'spatial', 'point', 'spatial', 'point', 'temporal', 'point', 'self-exciting', 'intuitively', 'self-exciting', 'point', 'time', 'point', 'point', 'point', 'self', 'point', 'simple', 'point', 'spatial', 'point', 'spatial', 'point', 'temporal', 'point', 'point', 'point', 'time', 'point', 'point', 'point', 'self', 'point', 'self', 'point', 'spatial', 'point', 'spatial', 'point', 'temporal', 'point', 'point', 'point', 'point', 'probability', 'point', 'point', 'point', 'self', 'point', 'self', 'point', 'simple', 'point', 'spatial', 'point', 'temporal', 'point', 'point', 'point', 'point', 'point', 'time', 'point', 'point', 'point', 'self', 'point', 'self', 'point', 'simple', 'point', 'spatial', 'point', 'temporal', 'point', 'point', 'point', 'stationary', 'point', 'stationary', 'point', 'stationary', 'point', 'time', 'point', 'random', 'point', 'typically', 'point', 'time', 'hawkes', 'marked', 'point', 'point', 'point', 'poisson', 'poisson', 'self', 'point', 'self', 'point', 'simple', 'point', 'spatial', 'point', 'spatial', 'point', 'physical', 'radioactive', 'stochastic', 'stochastic', 'stochastic', 'family', 'papoulis', 'stochastic', 'family', 'stochastic', 'random', 'brownian', 'brownian', 'stochastic', 'wiener', 'ito', 'wiener', 'poisson', 'intensity', 'wiener', 'levy', 'random', 'wiener', 'wiener', 'wiener', 'stochastic', 'increment', 'wiener', 'wiener', 'random', 'standard', 'stochastic', 'agreement', 'usual', 'hypothesis', 'stationary', 'analysis', 'generating', 'possibly', 'distribution', 'sample', 'random', 'probability', 'rise', 'probability', 'poisson', 'poisson', 'poisson', 'poisson', 'satisfying', 'poisson', 'discrete', 'point', 'poisson', 'random')
markoff	('chain', 'conditional', 'simplifies')
chain	('markoff', 'markov', 'markov', 'markov', 'collection', 'markov', 'papoulis', 'season', 'markov', 'markov', 'markov', 'markov', 'elements', 'markov', 'stochastic', 'markov', 'martingale', 'markov')
collection	('chain', 'random', 'data', 'function', 'non-explosive', 'case', 'space', 'modified', 'closed', 'random', 'point', 'replacement', 'containing')
index	('variable', 'runs', 'ruin', 'likelihood', 'number', 'further', 'set', 'space', 'number', 'set', 'major', ';', 'correlation', 'correlation', 'correlation', 'standard', 'correlation', 'regression', "laspeyres'", 'paasche', 'bowley', 'bowley', 'statistical', 'indices', "laspeyres'", 'paasche', 'fisher', 'fisher', 'statistical', 'indices', 'price', 'mean', 'statistical', 'indices', 'price', 'mean', 'statistical', 'indices', 'best-known', 'united', 'sort', 'respectively', 'fisher', 'geometric', 'harmonic', "laspeyres'", 'marshall-edgeworth', 'mitchell', 'paasche', 'walsh', 'walsh', 'number', 'bowley', 'fisher', 'fisher', 'geometric', 'mean', 'harmonic', 'mean', 'laspeyres', 'laspeyres', 'marshall', 'edgeworth', 'mitchell', 'mitchell', 'paasche', 'paasche', 'walsh', 'walsh', 'price', 'laspeyres', 'statistical', 'indices', 'price', 'edgeworth', 'statistical', 'indices', 'price', 'mitchell', 'statistical', 'indices', 'price', 'paasche', 'statistical', 'indices', 'price', 'walsh', 'statistical', 'indices', 'time', 'nonstationary', 'described', 'stability')
runs	('index', 'through', 'mean', 'eppes', 'cluster', 'two')
future	('present', 'process', 'probabilities', 'occurrence', 'occurrence', 'occurrence', 'time', 'linear', 'forecasting', 'forecast')
past	('other', 'sailing', 'six', 'sailing', 'six', 'refers', 'occurrence', 'occurrence', 'sailing', 'six', 'sailing', 'six')
take	('variate', 'discrete', 'size', 'paired', 'sign', 'paired', 'equivalent', 'probability', 'expected', 'value', 'value', 'equation', 'form', 'restricted', 'up', 'form', 'series', 'component', 'cumulant', 'developing', 'variable', 'continuous', 'variable', 'only', 'possibilities', 'value', 'argument')
walk	('example', 'random', 'unit', 'random', 'random', 'dimensional', 'mean', 'random', 'site', 'random', 'dimensional', 'martingale', 'random', 'results', 'holder', 'random', 'random', 'random', 'dimensional', 'wiener', 'trajectories', 'levy', 'levy', 'random', 'levy', 'lattice', 'random', 'random', 'random', 'watson', 'random', 'sequence', 'taken', 'random', 'portion', 'random', 'mathematical', 'dimension', 'confined', 'random', 'phenomenon', 'random', 'responsible', 'random', 'random', 'galton', 'random', 'dimensional', 'random', 'dimensional', 'random', 'dimensional', 'avoiding', 'self', 'avoiding', 'connective', 'change', 'followed', 'random', 'probability', 'random', 'one', 'random', 'dimensional', 'binomial', 'random', 'random', 'dimensional', 'random', 'dimensional', 'avoiding', 'wiener', 'random', 'unity', 'random', 'dimensional', 'pelya', 'random', 'random', 'dimensional', 'random', 'dimensional', 'random', 'less', 'random', 'random', 'dimensional', 'pelya', 'random', 'random', 'dimensional', 'random', 'dimensional', 'self-avoiding', 'path', 'self-avoiding', 'two-dimensional', 'self-avoiding', 'grid', 'small', 'self-avoiding', 'two-dimensional', 'avoiding', 'random', 'lattice', 'random', 'self', 'avoiding', 'connective', 'choice', 'hypercubic', 'up', 'self-avoiding', 'two', 'concatenating', 'necessarily', 'following', 'avoiding', 'connective', 'random', 'random', 'self', 'avoiding', 'wiener', 'wiener', 'random', 'random', 'ito', 'random', 'wiener', 'brownian', 'random', 'random', 'random', 'dimensional', 'random', 'residual', 'random', 'dimensional', 'random', 'random', 'dimensional')
features	('numb3rs', 'markov')
monte	('sequence', 'carlo', 'quasi', 'carlo', 'simulation', 'set', 'carlo', 'quasi', 'carlo')
carlo	('monte', 'method', 'quasi-monte', 'monte', 'integration', 'quasi-monte', 'quasi-monte', 'monte', 'method', 'monte', 'method')
recent	('most',)
stochastic	('value', 'type', 'matrix', 'nonsingular', 'matrices', 'nonsingular', 'nonsingular', 'matrices', 'group', 'distinct', 'matrices', 'nonsingular', 'small', 'matrices', 'over', 'nonsingular', 'over', 'matrix', 'doubly', 'matrix', 'chain', 'group', 'intensity', 'process', 'temporal', 'algorithm', 'uniform', 'synonymous', 'randomness', 'counterpart', 'involved', 'condition', 'random', 'variable', 'approximation', 'approximation', 'calculus', 'calculus', 'geometry', 'geometry', 'group', 'group', 'matrix', 'matrix', 'optimization', 'optimization', 'process', 'process', 'resonance', 'defines', 'process', 'p', 'process', 'function', 'process', 'real-valued', 'one', 'dimensional', 'process', 'theory', 'integral', 'interpreted', 'differential', 'quantum', 'parthasarathy', 'integration', 'quantum', 'calculus', 'quantum', 'processes', 'quantum', 'classical', 'differential', 'quantum', 'differential', 'quantum', 'calculus', 'continuous-time', 'process', 'dimensional', 'process')
doob	('processes', 'theorem', 'one-dimensional', 'space', 'papoulis', 'defines', 'theorem', 'random', 'time', 'theorem')
satisfy	('sequence', 'chapman-kolmogorov', 'mean', 'following', 'best', 'system', 'possibilities', 'possibilities', 'probabilities', 'papoulis', 'variate', 'lindeberg')
chapman-kolmogorov	('satisfy',)
governed	('distribution', 'markov', 'event', 'probability')
dependence	('smith', 'those')
transition	('probability', 'matrix')
substitution	('matrix', 'making', 'real')
characterize	('matrix', 'transitions', 'seeks', 'construct')
transitions	('characterize', 'finite')
closed	('number', 'deviation', 'random', 'random', 'set', 'random', 'set', 'collection', 'random', 'set', 'actually', 'function', 'solved', 'expressible', 'form', 'a089087', 'form', 'done', 'probability', 'region')
entries	('matrix', 'matrices', 'independent', 'size', 'consist', 'matrix', 'vary', 'matrices', 'independent', 'matrix', 'standard', 'random', 'taken', 'random', 'probability', 'probability', 'vector', 'probability', 'probability', 'mean', 'following', 'matrix', 'represent')
nonsingular	('two', 'stochastic', 'six', 'stochastic', 'set', 'stochastic', 'distinct', 'stochastic', 'stochastic', 'matrices', 'premultiplication', 'matrix', 'postmultiplication', 'matrix')
matrices	('stochastic', 'over', 'over', 'stochastic', 'over', 'stochastic', 'distinct', 'over', 'stochastic', 'over', 'nonsingular', 'over', 'entries', 'entries', 'real', 'function', 'probability', 'arising', 'dimensional', 'jodár', 'nonnegative', 'computationally', 'possible', 's')
mod	('integer', 'six')
six	('mod', 'nonsingular', 'past', 'inches', 'past', 'inches', 'furthermore', 'one', 'one', 'dice', 'one', 'chambers', 'revolver', 'chambers', 'revolver', 'chambers', 'past', 'inches', 'past', 'inches', 'clump', 'seven')
doubly	('processes', 'stochastic', 'noncentral', 'case', 'noncentral', 'function', 'noncentral')
horn	('matrix', 'theorem')
majorization	('theorem', 'markov')
integral	('above', 'stieltjes', 'normal', 'elliptic', 'first', 'taken', 'inner', 'rearranging', 'writing', 'odd', 'over', 'obtain', 'properly', 'set', 'domain', 'value', 'continuous', 'modulo', 'elliptic', 'first', 'stochastic', 'first', 'odd', 'use', 'physics', 'lerch', 'diverge', 'plugging', 'euler-mascheroni', 'gumbel', 'physics', 'lerch', 'value', 'normal', 'evaluating', 'find', 'gaussian', 'hh', 'probability', 'tetrachoric', 'probability', 'tetrachoric', 'inner', 'done', 'slowly')
stieltjes	('integral',)
feller	('function', 'wallace', 'berry', 'domain', 'average', 'modified', 'fee', 'modern', 'equal', 'fair', 'function', 'number', 'root', 'social', 'switches', 'de', 'function', 'beyer', 'due', 'value', 'theory', 'normal', 'lindeberg', 'central', 'hold', 'levy', 'zabell', 'lindeberg', 'variance', 'large', 'theorem', 'levy', 'lindeberg', 'central', 'theorem', 'levy', 'inequalities', 'kolmogorov', 'variance', 'strong', 'quantity')
normalized	('notation', 'kurtosis', 'form', 'weighting', 'linear', 'properly', 'function', 'probability', 'frequency', 'sample', 'sample', 'correlation', 'distribution', 'characteristic', 'angle', 'over', 'properly', 'raw', 'asymptotic', 'distribution', 'raw', 'density', 'properly', 'cumulative', 'form', 'function', 'function', 'mean', 'defining', 'raw', 'properly', 'th', 'distribution', 'sum', 'distribution', 'survival')
convolution	('wallace',)
wallace	('convolution', 'feller', 'series', 'integrating', 'cramer', 'szego', 'expansion', 'first')
berry	('feller', 'esseen', 'distribution', 'esseen', 'theorem', 'esseen', 'theorem', 'esseen', 'theorem', 'esseen')
esseen	('berry', 'theorem', 'berry', 'theorem', 'berry', 'theorem', 'berry', 'theorem', 'berry', 'theorem')
bessel	('correction', 'p', 'correction', 'moment', 'modified', 'function', 't', 'statistical', 'modified', 'function', 'modified', 'function', 'modified', 'function', 'modified', 'function', 'modified', 'function', 'distribution', 'statistical', 'modified', 'function', 'modified', 'function')
noted	('variance', 'kenney', 'fact', 'pointed')
probably	('factor', 'properly', 'model', 'pattern')
properly	('probably', 'attributed', 'what', 'integral', 'distribution', 'normalized', 'disappears', 'accounted', 'distribution', 'normalized', 'distribution', 'normalized', 'theta', 'normalized')
attributed	('properly',)
connection	('who', 'early', 'causal', 'diaconis', 'summarizes', 'results', 'unexpected', 'bell')
early	('connection', 'gauss')
univariate	('moment', 'probability', 'cumulant', 'subscript', 'bivariate', 'multivariate', 'variate', 'literature', 'hawkes', 'progress', 'self-exciting', 'brands', 'hawkes', 'version', 'process', 'function', 'hawkes', 'among', 'point', 'precisely', 'process', 'function', 'two', 'statistic', 'variate', 'multivariate', 'multivariate', 'multivariate', 'function', 'function', 'polynomial', 'anova', 'joins', 'distribution', 'distribution', 'unimodal', 'conversely', 'distribution')
those	('moment', 'taken', 'moment', 'taken', 'green', 'intersecting', 'yellow', 'intersecting', 'red', 'missing', 'sum', 'among', 'listed', 'dependence')
binomial	('using', 'distribution', 'inverse', 'distribution', 'negative', 'multivariate', 'distribution', 'multivariate', 'distribution', 'calculate', 'explicitly', 'variable', 'parameter', 'left', 'factorial', 'walk', 'distribution', 'integer', 'integer', 'occur', 'term', 'distribution', 'series', 'distribution', 'discrete', 'variate', 'distribution', 'distribution', 'moment', 'approximation', 'discrete', 'distribution', 'distribution', 'similar', 'definition', 'negative', 'trial', 'distribution', 'negative', 'distribution', 'beta', 'distribution', 'distributed', 'function', 'beta', 'distribution', 'distribution', 'distribution', 'distribution', 'probability', 'distribution', 'distribution', 'trial', 'distribution', 'observed', 'distribution', 'function', 'distribution', 'approximation', 'distribution', 'distribution', 'distribution', 'infinity', 'distribution', 'independent', 'random', 'distribution', 'distribution', 'distribution', 'de', 'negative', 'distribution', 'distribution', 'distribution', 'negative', 'distribution', 'rise', 'distribution', 'distribution', 'distribution', 'distribution', 'negative', 'function', 'negative', 'distribution', 'negative', 'distribution', 'distribution', 'distribution', 'limit', 'distribution', 'distribution')
transform	('papoulis', 'probability', 'probability', 'fourier', 'kurtosis', 'papoulis', 'two-dimensional', 'practice', 'data', 'matrix', 'form', 'taken', 'fourier', 'exponential', 'probability', 'taken', 'expand', 'fourier', 'gaussian', 'fourier', 'gaussian')
transformations	('moment', 'using', 'case', 'using', 'example', 'using', 'moment', 'variance', 'term', 'using', 'example', 'using')
multivariate	('moment', 'probability', 'similarly', 'central', 'term', 'n', 'derive', 'expression', 'central', 'term', 'operator', 'moment', 'probability', 'similarly', 'raw', 'term', 'one', 'bivariate', 'distribution', 'univariate', 'distribution', 'normal', 'analysis', 'findclusters', 'point', 'definition', 'hawkes', 'one', 'value', 'hawkes', 'different', 'hawkes', 'type', 'function', 'hawkes', 'function', 'function', 'distribution', 'normal', 'vector', 'bivariate', 'bivariate', 'bivariate', 'analysis', 'analysis', 'binomial', 'calculus', 'distribution', 'distribution', 'function', 'function', 'normal', 'distribution', 'orthogonal', 'polynomial', 'polynomial', 'polynomial', 'resultant', 'resultant', 'normal', 'denoted', 'normal', 'function', 'normal', 'numerically', 'normal', 'normal', 'distribution', 'normal', 'univariate', 'univariate', 'bivariate', 'univariate', 'normal', 'distribution', 'binomial', 'number', 'variate', 'matrix', 'probabilistic', 'fitting', 'analysis', 'sum', 'generalization', 'statistic', 'case', 'form', 'distribution', 'theorem', 'interval', 'form', 'similarly', 'distribution')
subset	('larger', 'kolmogorov', 'general', 'denoted', 'containing', 'denotes', 'distribution', 'denotes', 'ambient', 'stationary', 'joint', 'nested', 'certain', 'probability', 'outcome', 'probability', 'sample')
larger	('subset', 'table', 'difference', 'vi')
indicator	('function', 'function')
identically	('function', 'one', 'variable', 'distributed', 'independent', 'normally', 'independent', 'distributed')
elsewhere	('characteristic',)
iverson	('using', 'cumulant', 'bracket')
bracket	('useful', 'iverson', 'moment', 'moment')
devices	('descriptive', 'easier')
repeating	('function',)
fourier	('denoted', 'using', 'function', 'using', 'function', 'transform', 'inverse', 'function', 'distribution', 'using', 'transform', 'inverse', 'obtain', 'inverse', 'expand', 'form', 'transform', 'theorem', 'transform')
abramowitz	('moment', 'stegun', 'cumulant', 'stegun', 'notation;', 'stegun', 'denoted', 'stegun', 'unfortunately', 'stegun', 'p', 'stegun', 'p', 'stegun', ';', 'stegun', ';', 'stegun', 'value', 'stegun', 'function', 'stegun', 'distribution', 'stegun', 'function', 'stegun', 'place', 'stegun', 'distribution', 'stegun', 'factor', 'stegun', 'value', 'stegun', ';', 'stegun', 'function', 'stegun')
stegun	('abramowitz', 'abramowitz', 'abramowitz', 'abramowitz', 'abramowitz', 'confusingly', 'abramowitz', 'abramowitz', 'abramowitz', 'probability', 'abramowitz', 'prevost', 'abramowitz', 'abramowitz', 'abramowitz', 'abramowitz', 'abramowitz', 'johnson', 'abramowitz', 'abramowitz', 'abramowitz', 'abramowitz', 'prevost', 'abramowitz')
morrison	('p', 'statistical')
uniquely	('distribution', 'specified', 'distribution', 'specified', 'net', 'determined', 'outcome', 'determined')
converges	('function', 'absolutely', 'actual')
absolutely	('converges', 'near', 'number', 'fair', 'variate', 'fair', 'p', 'fair', 'large', 'sure')
near	('absolutely', 'origin')
origin	('near', 'papoulis', 'star', 'greek', 'pelya', 'first', 'first', 'never', 'independent')
generate	('function', 'raw', 'single', 'sequence', 'order', 'power-law', 'approach', 'sequence', 'average', 'irregular', 'wish')
generating	('moment', 'function', 'cumulant', 'function', 'cumulant', 'function', 'cumulant', 'function', 'moment', 'function', 'cumulant', 'function', 'moment', 'function', 'moment', 'function', 'cumulant', 'function', 'method', 'probability', 'point', 'method', 'pseudorandom', 'sphere', 'random', 'number', 'mean', 'effect', 'pair', 'well', 'coefficient', 'process', 'exponential', 'value', 'function', 'expression')
check	('verify', 'charlier', 'use', 'charlier', 'charlier', 'charlier', 'cumulant', 'charlier', 'covariance', 'covariance')
verify	('check', 'correct')
well	('computed', 'rescaled', 'observation', 'construct', 'distributed', 'relation', 'generating', 'noonan', 'inverted', 'very', 'distribution', 'voit', 'necessary')
rescaled	('well', 'frequencies')
charlier	('data', 'check', 'pass', 'check', 'check', 'function', 'check', 'moment', 'check', 'series', 'series', 'chebyshev', 'edgeworth', 'szego', 'series', 'expansion', 'series', 'sum', 'expansion', 'series')
added	('column', 'right', 'sequence', 'two', 'probabilities', 'factor', 'transforming')
identity	('noting', 'connects', 'multiplication', 'cards', 'permutation', 'distance', 'time', 'operations', 'operations', 'matrix', 'formal', 'pairwise', 'pairwise', 'differential', 'been', 'fraction', 'simple')
connects	('identity', 'fundamental', 'classical')
seven	('checked', 'six')
checked	('seven',)
correctly	('example', 'newton', 'opined')
pass	('computation', 'charlier', 'angle', 'over')
strength	('measure', 'correlation', 'measure', 'associations', 'correlation', 'relationship')
correlation	('strength', 'two', 'covariance', 'distribution', 'coefficient', 'statistical', 'variance', 'statistical', 'kenney', 'variance', 'transformation', 'coefficient', 'independent', 'exist', 'general', 'rank', 'rank', 'coefficient', 'pearson', 'rank', 'coefficient', 'exact', 'rank', 'coefficient', 'rank', 'coefficient', 'statistic', 'coefficient', 'independent', 'exist', 'successive', 'rank', 'coefficient', 'rank', 'coefficient', 'degree', 'degree', 'quantified', 'autocorrelation', 'regression', 'autocorrelation', 'coefficient', 'cross', 'geometric', 'geometric', 'recurrence', 'statistical', 'pearson', 'coefficient', 'product-moment', 'coefficient', 'quantity', 'data', 'coefficient', 'coefficient', 'denoted', 'coefficient', 'coefficient', 'pearson', 'pearson', 'above', 'coefficient', 'square', 'coefficient', '◇', 'coefficient', 'scale', 'coefficient', 'regression', 'index', 'index', 'coefficient', 'distribution', 'ratio', 'rank', 'coefficient', 'distribution', 'population', 'probability', 'multiple', 'eckhardt', 'coefficient', 'regression', 'coefficient', 'rank', 'coefficient', 'regression', 'index', 'p', 'index', 'regression', 'coefficient', 'sample', 'ratio', 'population', 'pp', 'ratio', 'regression', 'coefficient', 'quantity', 'anova', 'coefficient', 'regression', 'coefficient', 'confused', 'variate', 'denotes', 'general', 'strength', 'statistical', 'regression', 'method', 'bland', 'agreement', 'fèvre', 'mean', 'mean', 'coefficient', 'eigenvalue', 'mean', 'coefficient', 'normalized', 'distribution', 'coefficient', 'cross', 'coefficient', 'distribution', 'coefficient', 'form', 'function', 'student', 'matrix', 'theorem', 'coefficient')
respective	('value', 'point')
explicitly	('out', 'uncorrelated', 'written', 'computed', 'binomial', 'term', 'law', 'spencer', 'function', 'order', 'find', 'first', 'central', 'first', 'first', 'central', 'first')
correlated	('variable', 'covariance', 'highly', 'manner', 'highly', 'manner', 'nine', 'matrix', 'perfectly', 'perfectly')
increase	('tends', 'actuality', 'average', 'significance', 'student', 'percentage')
decrease	('tends', 'series', 'thompson')
converse	('uncorrelated', 'necessarily', 'uncorrelated', 'necessarily', 'uncorrelated', 'necessarily', 'cramer', 'namely', 'fisher', 'independent', 'theorem')
necessarily	('converse', 'function', 'probability', 'converse', 'walk', 'maintain', 'even', 'curve', 'straight', 'converse', 'distribution', 'differentiating', 'need', 'same')
reduces	('covariance', 'usual', 'model', 'classical', 'expected', 'square', 'equation', 'classical')
usual	('reduces', 'domain', 'established', 'whereas', 'approach', 'true', 'process', 'convention', 'definition', 'become', 'encountered', 'notation')
motivates	('variance', 'use')
symbol	('use', 'variance', 'parameter', 'moment-generating', 'use', 'above', 'beyer')
consistent	('provide', 'denoting', 'function', 'widespread', 'certainly', 'integer', 'row', 'proposition')
derived	('deviation', 'quantity', 'above', 'noting', 'term', 'kac', 'kac', 'matrix', 'kanzieper', 'case', 'true', 'independently', 'gauss', 'parameter', 'variance', 'using', 'student', 'transforming')
looking	('useful', 'despite', 'ill-behaved')
identities	('obey', 'procedure', 'kendall')
induction	('covariance', 'definition', 'analogous')
bivariate	('moment', 'normal', 'univariate', 'multivariate', 'statistic', 'distribution', 'distribution', 'normal', 'normal', 'function', 'normal', 'unit', 'derive', 'normal', 'function', 'normal', 'standardized', 'normal', 'similarly', 'normal', 'coefficient', 'normal', 'multivariate', 'multivariate', 'statistic', 'multivariate', 'generalization', 'normal', 'distribution', 'normal', 'distribution', 'normal', 'many', 'statistic', 'multivariate', 'describing', 'two-dimensional', 'normal', 'distribution', 'normal', 'ppmcc', 'coefficient', 'normal', 'normal', 'coefficient', 'normal', 'distribution', 'normal', 'distribution', 'distribution', 'distribution', 'normal', 'distribution', 'normal', 'function', 'normal', 'normal', 'covariance', 'normal', 'example', 'distribution', 'distribution')
maclaurin	('p', 'approximation')
cumulant-generating	('variable', 'function', 'function', 'function', 'excess', 'pp', 'seen')
graph	('coefficient', 'nodes', 'vertices', 'excess', 'cage', 'kurtosis', 'moore', 'statistic', 'skewness', 'probability', 'likelihood', 'likelihood', 'vertices-edges', 'buekenhout', 'net', 'polyhedron', 'bar', 'plot', 'line', 'showing', 'analysis', 'smoothing')
nodes	('graph',)
girth	('biggs',)
biggs	('girth', 'ito')
ito	('biggs', 'wong', 'process', 'lemma', 'kiyoshi', 'spelled', 'spelled', 'noboru', 'lemma', 'integration', 'basic', 'use', 'formula', 'definition', 'multiplication', 'walk', 'lemma')
wong	('ito', 'cage')
cage	('wong', 'moment', 'graph')
minimal	('vertices', 'a033810', 'number', 'a052944', 'distinct', 'toss')
factorial	('moment', 'moment', 'function', 'moment', 'probability', 'binomial', 'approximately', 'first')
gamma	('deviation', 'statistic', 'function', 'distribution', 'distribution', 'f-distribution', 'skewness', 'statistic', 'distribution', 'distribution', 'incomplete', 'function', 'expansion', 'function', 'distribution', 'distribution', 'distribution', 'characteristic', 'regularized', 'distribution', 'freedom', 'incomplete', 'regularized', 'obey', 'fisher', 'distribution', 'complete', 'incomplete', 'closely', 'distribution', 'distribution', 'incomplete', 'function', 'function', 'function', 'function', 'ratio', 'distribution', 'distribution', 'distribution', 'relevant', 'complete', 'incomplete', 'function', 'distribution', 'regularized', 'excess', 'distribution', 'variate', 'distribution', 'distributed', 'variate', 'distribution', 'distribution', 'distribution', 'parameter', 'distribution', 'standard', 'variate', 'parameter', 'distribution', 'moment', 'function', 'incomplete', 'noncentral', 'student', 'distribution', 'moment', 'iii', 'p', 'moment', 'freedom', 'excess', 'function', 'function', 'incomplete')
heteroscedastic	('variance', 'moment', 'residual')
homoscedastic	('moment', 'variance', 'variance')
operator	('derive', 'kendall', 'multivariate', 'unitary', 'tensor', 'unitary', 'ampliation', 'commutation', 'relation', 'processes', 'most')
derive	('operator', 'multivariate', 'example', 'expression', 'coefficient', 'bivariate', 'name')
expression	('derive', 'multivariate', 'desired', 'slightly', 'uspensky', 'remarkably', 'independent', 'sum', 'monotonicity', 'plugging', 'asymptotic', 'exact', 'equation', 'logarithmic', 'analogous', 'product', 'set', 'solve', 'generating')
rewrite	('begin', 'variable', 'function', 'summand')
differentiate	('obtain', 'side')
wherever	('side', 'term')
remove	('derivative', 'derivative', 'continuous', 'diminish')
replace	('derivative', 'argument')
argument	('replace', 'correct', 'actually', 'depend', 'zero', 'take', 'over')
appearing	('s', 'power', 'term', 'constant', 'random', 'biology', 'issue', 'fisher')
finally	('set', 'plugging', 'obtain', 'tosses')
interpret	('coefficient',)
subscript	('time', 'univariate', 'indicate')
iterating	('case', 'above', 'generator', 'value', 'logistic')
fourth	('form', 'central', 'ane', 'third', 'two', 'fifth')
flavors	('several',)
encountered	('most', 'variety', 'distribution', 'frequently', 'mathematical', 'fisher', 'kenney', 'frequently', 'measure', 'tth', 'before', 'most', 'pseudoinverse', 'widely', 'usual')
normally	('variety', 'termed', 'moment', 'data', 'function', 'independently', 'themselves', 'distributed', 'distributed', 'kac', 'increments', 'asymptotically', 'identically', 'standard', 'variance', 'two', 'error', 'distributed', 'two', 'independent', 'two', 'sum', 'generally', 'function', 'independent', 'independent', 'distributed', 'infinite', 'distributed', 'purely', 'variate', 'approximately')
termed	('normally', 'kurtosis')
notation;	('pearson', 'abramowitz')
dist	('kurtosis', 'sample', 'meaning')
unfortunately	('abramowitz', 'notation', 'term', 'quantity', 'because', 'term')
confusingly	('stegun', 'many', 'p', 'skewness')
positive	('practice', 'sharper', 'constant', 'possibly', 'step', 'horizontal', 'step', 'horizontal', 'a086253', 'root', 'a086254', 'root', 'alpha', 'predictive', 'test', 'true', 'getting', 'test', 'produce', 'statistical', 'false', 'false', 'test', 'true', 'true', 'false', 'alpha', 'false', 'false', 'set', 'function', 'parameter', 'quantity')
sharper	('positive', 'peak')
reason	('likely', 'kurtosis', 'deviation', 'biased', 'insufficient', 'probability', 'no', 'believe', 'no', 'predicating', 'insufficient', 'insufficient', 'probability', 'insufficient', 'pseudorandom', 'standard')
historically	('excess', 'detailed', 'detailed')
incorrectly	('regarded', 'function', 'spurious', 'skewness', 'spurious', 'combining', 'argue', 'central')
correspondence	('distribution', 'kurtosis')
peakedness	('kurtosis', 'true', 'infinite', 'negative', 'degree', 'kaplansky')
general;	('true',)
perfectly	('distribution', 'flat', 'either', 'correlated', 'correlated', 'anticorrelated', 'ball')
flat	('perfectly', 'top')
negative	('peakedness', 'kurtosis', 'distribution', 'binomial', 'estimator', 'likelihood', 'sequence', 'recurrence', 'test', 'likelihood', 'term', 'likelihood', 'nlr', 'likelihood', 'statistic', 'predictive', 'test', 'test', 'false', 'false', 'test', 'test', 'statistic', 'false', 'true', 'false', 'manova', 'likelihood', 'false', 'success', 'binomial', 'distribution', 'binomial', 'distribution', 'binomial', 'distribution', 'binomial', 'binomial', 'function', 'binomial', 'relation', 'binomial')
kaplansky	('peakedness', 'kenney')
westfall	('p', 'kurtosis')
determining	('useful', 'asymmetry', 'method', 'fit', 'test', 'probability')
tailedness	('asymmetry',)
geometric	('mean', 'mean', 'arithmetic', 'mean', 'centroid', 'mean', 'distribution', 'arithmetic', 'mean', 'mean', 'mean', 'harmonic', 'mean', 'mean', 'mean', 'distribution', 'win', 'ruin', 'distribution', 'tetrahedron', 'correlation', 'correlation', 'unit', 'mean', 'index', 'mean', 'index', 'mean', 'analog', 'distribution', 'distribution', 'distribution', 'trial', 'tossing', 'distribution', 'distribution', 'distribution', 'distribution', 'function', 'distribution', 'cumulant', 'distribution', 'deviation', 'distribution', 'function', 'distribution', 'distribution', 'series', 'integer', 'type', 'definition', 'become', 'distribution', 'distribution')
arithmetic-geometric	('mean', 'mean')
root-mean-square	('applied', 'quantity', 'distribution', 'abbreviated', 'interval', 'interval', 'special', 'term', 'synonym', 'synonym', 'deviation', 'value', 'distance')
again	('mean', 'applied', 'deviation', 'data', 'chambers', 'ignoring', 'point', 'one', 'derivative', 'dropping', 'set')
complete	('elements', 'elliptic', 'distribution', 'constant', 'elliptic', 'regression', 'event', 'gamma', 'change', 'gamma', 'even', 'solution')
macron	('notation',)
homogeneous	('mean', 'case', 'first')
centroid	('analogous', 'function', 'geometric', 'median', 'opposite', 'triangle', 'triangle')
analogous	('centroid', 'quantity', 'increased', 'technique', 'technique', 'red', 'expression', 'induction', 'results')
joke	('mean', 'told', 'exclaim', 'data', 'told', 'exclaim', 'maintained')
told	('joke', 'mean', 'joke')
statisticians	('two', 'out', 'two', 'one')
hunting	('out', 'one', 'out', 'one')
sees	('one',)
duck	('first', 'mean', 'first', 'approximately')
aim	('first', 'statistician', 'first', 'statistician')
shoots	('bullet', 'time', 'bullet', 'time')
bullet	('shoots', 'goes', 'time', 'goes', 'shoots', 'goes', 'time', 'goes')
goes	('bullet', 'sailing', 'bullet', 'sailing', 'bullet', 'sailing', 'bullet', 'sailing', 'value')
sailing	('goes', 'past', 'goes', 'past', 'goes', 'past', 'goes', 'past')
inches	('six', 'too', 'six', 'too', 'six', 'too', 'six', 'too')
statistician	('second', 'aim', 'out', 'second', 'aim', 'one', 'mathematicians')
exclaim	('joke', 'joke')
shots	('two', 'hit', 'two', 'hit')
hit	('shots', 'shots', 'potentially', 'ball', 'one')
lehmer	('mean', 'mean', 'mean')
root	('mean', 'mean', 'namely', 'moment', 'mean', 'mean', 'mean', 'fit', 'mean', 'square', 'sample', 'square', 'bias-corrected', 'mean', 'distribution', 'mean', 'square', 'estimated', 'square', 'square', 'variance', 'positive', 'above', 'positive', 'above', 'modified', 'feller', 'square', 'chi-squared', 'multiplication', 'multiplication', 'possible', 'beta')
stolarsky	('deviation', 'mean', 'trimean')
natural	('deviation', 'intuitive', 'moment', 'less', 'map', 'domain', 'function', 'logarithm', 'logarithm', 'unique', 'invariance', 'function')
intuitive	('natural', 'definition')
introduction	('deviation', 'absolute')
analytical	('value',)
rely	('technique', 'minimizing')
minimizing	('rely', 'sum', 'point', 'sum', 'derivative', 'amenable', 'addition', 'second-')
residuals	('square', 'sum')
straightforward	('deviation', 'obtain', 'relatively', 'extension')
hand	('mean', 'equation', 'authors')
unwieldy	('form', 'breaking', 'years', '◇', 'form', 'computationally', 'large')
breaking	('unwieldy', 'up', 'lattice', 'self-avoiding')
summand	('up', 'two', 'rewrite', 'processes')
pieces	('two', 'treating')
treating	('pieces', 'expansion', 'distribution')
separately	('following', 'symbolically', 'considering', 'indicated', 'sum')
named	('deviation', 'continuous', 'deviation', 'discrete', 'centered', 'norbert', 'distribution', 'using', 'experiment', 'english')
incomplete	('distribution', 'beta', 'upper', 'gamma', 'function', 'gamma', 'function', 'gamma', 'moment', 'gamma', 'function', 'gamma', 'papoulis', 'gamma', 'function', 'beta', 'function', 'beta', 'constant', 'gamma')
beta	('incomplete', 'function', 'md', 'distribution', 'function', 'distribution', 'p', 'distribution', 'function', 'regularized', 'function', 'distribution', 'distribution', 'distributed', 'distribution', 'function', 'variate', 'prime', 'distribution', 'distribution', 'probability', 'weibull-type', 'extreme', 'function', 'regularized', 'distribution', 'function', 'regularized', 'function', 'variate', 'prime', 'distribution', 'distribution', 'distribution', 'prime', 'distribution', 'parameter', 'distribution', 'function', 'variate', 'prime', 'distribution', 'prime', 'distribution', 'distribution', 'probability', 'function', 'function', 'function', 'i', 'root', 'prime', 'function', 'distribution', 'distribution', 'function', 'regularized', 'raw', 'variable', 'binomial', 'distribution', 'function', 'variance', 'binomial', 'distribution', 'distribution', 'distribution', 'incomplete', 'incomplete', 'regularized')
euler-mascheroni	('function', 'length', 'moment', 'plugging', 'integral', 'excess', 'maximum', 'analytically')
constant	('meijer', 'positive', 'physical', 'adapted', 'reversion', 'time', 'havil', 'whenever', 'same', 'appearing', 'm', 'independent', 'complete', 'random', 'connective', 'random', 'random', 'random', 'random', 'connective', 'staircase', 'connective', 'beyer', 'connective', 'random', 'common', 'either', 'above', 'interpreting', 'kolakoski', 'run', 'nonnegative', 'success', 'apery', 'central', 'apery', 'distribution', 'definition', 'wolfram', 'higher', 'distribution', 'probability', 'hypergeometric', 'joint', 'harmonic', 'distribution', 'incomplete', 'general')
meijer	('constant', 'term')
g-function	('exponential', 'plotted')
exponential	('g-function', 'distribution', 'distribution', 'bring', 'outside', 'rate', 'function', 'sum', 'span', 'respectively', 'processes', 'domain', 'processes', 'domain', 'fitting', 'least', 'fitting', 'regression', 'fitting', 'least', 'fitting', 'least', 'moving', 'exponentially', 'moving', 'sum', 'moving', 'distribution', 'distribution', 'simplifies', 'distribution', 'distribution', 'lambda', 'distribution', 'generalized', 'probability', 'excess', 'distribution', 'double', 'distribution', 'identical', 'transform', 'distribution', 'distribution', 'believe', 'law', 'analog', 'a000629', 'generating', 'equivalently', 'distribution', 'distribution', 'outer')
md	('beta', 'bernoulli')
gumbel	('distribution', 'distribution', 'type', 'integral', 'distribution', 'distribution', 'distribution', 'distribution', 'type', 'minimum', 'distribution', 'connecting', 'distribution', 'inverse', 'distribution', 'distribution', 'distribution')
half-normal	('distribution', 'distribution', 'distribution', 'distribution')
laplace	('distribution', 'distribution', 'solution', 'pp', 'buffon', 'needle', 'buffon', 'needle', 'buffon', 'needle', 'buffon', 'needle', 'moivre', 'theorem', 'distribution', 'distribution', 'excess', 'distribution', 'subsequently', 'study', 'moivre', 'theorem')
logistic	('distribution', 'iterating', 'distribution', 'distribution', 'continuous', 'name', 'distribution', 'excess', 'distribution', 'distribution', 'equation', 'uniform')
maxwell	('distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'function', 'distribution', 'distribution', 'distribution')
pareto	('distribution', 'histogram', 'plot', 'plot', 'categories', 'statisticalplots`', 'plot', 'distribution', 'distribution', 'excess', 'distribution')
rayleigh	('distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'function', 'distribution', 'reduce', 'distribution', 'distribution')
displacement	('square', 'square', 'random', 'square', 'square', 'power', 'random', 'square', 'over')
msd	('set', 'directions', 'mean', 'random')
displacements	('set', 'particularly')
brownian	('particularly', 'motion', 'process', 'motion', 'everywhere', 'motion', 'criteria', 'motion', 'moreover', 'motion', 'glance', 'contrarily', 'motion', 'higher-dimensional', 'independent', 'process', 'motion', 'start', 'motion', 'one-dimensional', 'representation', 'motion', 'functional', 'motion', 'phenomenon', 'independent', 'motion', 'standard', 'indeed', 'walk', 'motion')
motion	('brownian', 'random', 'brownian', 'brownian', 'standard', 'brownian', 'number', 'brownian', 'satisfies', 'holder', 'brownian', 'nowhere', 'start', 'brownian', 'brownian', 'random', 'integration', 'brownian', 'poisson', 'brownian', 'poisson', 'collisions', 'brownian', 'random', 'denotes', 'essentially', 'brownian', 'independent', 'indeed')
two-dimensional	('problem', 'random', 'transform', 'continuous', 'distribution', 'bivariate', 'hammersley', 'number', 'normal', 'sum', 'proven', 'walk', 'square', 'walk', 'square', 'linearly', 'variable', 'function', 'copula', 'distribution', 'function', 'distribution')
directions	('msd', 'allowed', 'step', 'number', 'certain')
dimensional	('walk', 'counting', 'walk', 'saint', 'walk', 'stochastic', 'walk', 'random', 'walk', 'random', 'walk', 'self', 'walk', 'random', 'walk', 'random', 'walk', 'self', 'walk', 'random', 'walk', 'random', 'walk', 'walk', 'random', 'walk', 'random', 'walk', 'walk', 'stochastic', 'appropriately', 'matrices', 'walk', 'walk')
moment-generating	('using', 'value', 'independent', 'function', 'logarithm', 'first', 'parameter', 'using', 'logarithmic', 'symbol', 'distribution', 'using', 'simplifies', 'function', 'function', 'p', 'discreteuniformdistribution', 'function', 'solved', 'change')
standardized	('deviation', 'moment', 'third', 'first', 'moment', 'p', 'bivariate', 'function', 'trivariate', 'distribution', 'function', 'normal')
differentiable	('satisfies', 'almost', 'continuous', 'function')
simpler	('moment', 'work', 'value', 'poorer', 'provide', 'analytic', 'rewritten', 'form', 'provide', 'analytic', 'via', 'obtain')
conditions	('what', 'possible', 'sufficient', 'sequence', 'th')
bounded	('function', 'variation', 'function', 'variation', 'moment', 'space', 'linear', 'system', 'flow', 'system')
hausdorff	('sequence', 'first')
necessary	('obtain', 'sufficient', 'estimator', 'sample', 'boundary', 'normalize', 'well')
sufficient	('necessary', 'conditions', 'lindeberg-feller', 'condition', 'criterion', 'condition')
momental	('skewness', 'skewness', 'skewness', 'range', 'skewness', 'mean', 'skewness')
spurious	('incorrectly', 'multiplicative', 'incorrectly', 'multiplicative', 'lot', 'lot')
multiplicative	('spurious', 'factor', 'spurious', 'factor', 'modulo', 'additive')
loading	('data', 'package', 'data', 'package')
statistics`descriptivestatistics`	('measure', 'pearson')
suggested	('measure', 'karl')
karl	('suggested', 'due', 'size', 'pearson')
iii	('type', 'pearson', 'type', 'type', 'distribution', 'gamma', 'type', 'distribution')
exponentiating	('cumulant',)
robbin	('variance', 'inequality', 'dvoretzky', 'variance', 'mannion', 'palasti')
abbreviated	('root-mean-square', 'quadratic', 'process', 'average', 'ema', 'function', 'function')
quadratic	('abbreviated', 'algebra', 'suppose', 'form')
domain	('over', 'term', 'term', 'most', 'value', 'function', 'feller', 'function', 'usual', 'divisors', 'probability', 'integral', 'map', 'natural', 'one', 'one', 'probability', 'range', 'reinhardt', 'statistical', 'probability', 'interval', 'probability', 'probability', 'space', 'measurable', 'triple', 'measurable', 'value', 'distribution', 'function', 'probability', 'exponential', 'second', 'exponential', 'fundamental', 'self-avoiding', 'ranging', 'probability', 'statistic', 'probability', 'limited', 'probability', 'function', 'range', 'precise', 'distribution', 'image')
periodic	('function', 'over')
hoehn	('mean', 'niven')
niven	('hoehn',)
physical	('constant', 'use', 'list', 'use', 'random', 'process', 'unpredictable', 'important', 'depend', 'properties')
synonym	('root-mean-square', 'standard', 'root-mean-square', 'standard')
signal	('deviation', 'baseline', 'term', 'processing', 'measurement', 'discrete', 'infinite-precision', 'band-limited', 'nyquist')
baseline	('signal', 'standard')
pythagorean	('mean',)
storing	('determined', 'set')
recursion	('using', 'relationship', 'regression', 'regression', 'fitting', 'regression', 'self', 'using', 'relation')
involving	('relationship', 'only', 'two', 'mean', 'many', 'one', 'system', 'weibull')
precomputed	('only',)
optimal	('less', 'notation', 'case', 'situations')
bias-corrected	('value', 'sample', 'root', 'variance', 'notation', 'sample')
recurrence	('using', 'equation', 'using', 'linear', 'example', 'correlation', 'plot', 'a042942', 'following', 'sequence', 'negative', 'only', 'general', 'written', 'cumulant', 'cumulant', 'cumulant')
working	('equation', 'first', 'obtain', 'first')
◇	('work', 'considering', 'desired', 'remains', 'third', 'kenney', 'long', 'written', 'equating', 'correlation', 'overall', 'long-dashed', 'fair', 'unwieldy', 'large')
considering	('◇', 'third', 'separately')
plugging	('finally', 'term', 'kenney', 'solving', 'conditional', 'writing', 'back', 'writing', 'back', 'et', 'expression', 'distribution', 'using', 'become', 'integral', 'euler-mascheroni')
desired	('◇', 'expression')
algebra	('p', 'deriving', 'find', 'simplified', 'random', 'sigma', 'state', 'quadratic')
deriving	('algebra', 'equation')
tedious	('performed',)
already	('value', 'equation', 'event', 'occurred', 'probability')
remains	('◇', 'only', 'observation', 'true')
simplified	('algebra', 'considerably')
considerably	('simplified', 'immediately')
immediately	('considerably', 'transforming', 'identical', 'eliminating')
transforming	('immediately', 'fèvre', 'data', 'added', 'kenney', 'derived')
transformed	('using', 'set', 'number', 'random')
eliminating	('immediately', 'expectation')
containing	('term', 'odd', 'subset', 'accumulation', 'urn', 'two', 'collection', 'indistinguishable', 'square', 'number')
expand	('equal', 'equation', 'choose', 'transform', 'fourier')
ane	('third', 'fourth')
student	('computed', 'conjectured', 'seemed', 'moment', 'first', 'modern', 'hardly', 'test', 'testing', 'wilcoxon', 'snedecor', 'snedecor', 'uniform', 'distribution', 'generalization', 'noncentral', 'noncentral', 'gamma', 'noncentral', 't', 'distribution', 'distribution', 'distribution', 'variance', 'distribution', 'knowing', 'increase', 'normal', 'distribution', 'derived', 'excess', 'characteristic', 'form', 'correlation', 'distributed', 'freedom', 't', 'distribution', 'noncentral', 'paired', 'paired', 'function', 'cumulative', "student'", 'z', 'distribution')
conjectured	('student', 'underlying', 'appear', 'parker', 'amazingly', 'lattice', 'madras', 'been', 'mean', 'been', 'self', 'palasti', 'two')
conjecture	('function', 'subsequently', 'concave', 'shephard', 'unfolding', 'hypothesis', 'hypothesis', 'continuum')
subsequently	('conjecture', 'proven', 'distribution', 'laplace')
proven	('subsequently', 'equal', 'using', 'teth', 'no', 'been', 'two-dimensional', 'been')
varying	('above', 'sample')
distributed	('data', 'independently', 'normally', 'variable', 'distribution', 'immigrants', 'inhomogeneous', 'immigrants', 'independent', 'independently', 'below', 'uniformly', 'unit', 'independent', 'normally', 'uniformly', 'uniformly', 'unit', 'uniformly', 'variate', 'variate', 'variate', 'random', 'uniformly', 'pseudorandom', 'random', 'well', 'point', 'independently', 'equal', 'expectation', 'uniformly', 'slope', 'identically', 'mean', 'variance', 'kolmogorov-smirnov', 'variate', 'beta', 'variate', 'variance', 'independently', 'distribution', 'freedom', 'variate', 'parameter', 'gamma', 'variable', 'appropriate', 'independently', 'noncentral', 'normally', 'mean', 'cauchy', 'independent', 'new', 'normally', 'normally', 'universe', 'independent', 'snedecor', 'random', 'independent', 'student', 'distribution', 'binomial', 'number', 'using', 'uniformly', 'value', 'variable', 'inverse', 'kallenberg', 'central', 'form', 'freedom', 'identically', 'random')
corrected	('moment', 'interval', 'first')
ungrouped	('cumulant', 'distribution')
restrictive	('under',)
proof	('see', 'catherine', 'important', 'six-line', 'central', 'cumbersome', 'central')
see	('proof', 'kendall', 'needle-tossings', 'badger', 'wait', 'string', 'wait', 'probability', 'interpretation', 'value', 'before', 'bevington', 'wanted', 'pearson', 'craig', 'derivation', 'papoulis', 'sure', 'incredibly')
pronounced	('distribution', 'right')
reverse	('skewness', 'data')
confusing	('skewness', "wasn't")
due	('notation', 'karl', 'p', 'model', 'vast', 'practice', 'only', 'martingale', 'theorem', 'noboru', 'value', 'approximation', 'surprising', 'notation', 'feller', 'approximation', 'bagby', 'value', 'blaisdell')
f-distribution	('gamma', 'vector')
hypergeometric	('distribution', 'coefficient', 'regularized', 'regularized', 'eigenvalue', 'coefficient', 'confluent', 'limit', 'number', 'distribution', 'probability', 'confluent', 'function', 'moment', 'confluent', 'function', 'function', 'confluent', 'limit', 'function', 'confluent', 'function', 'regularized', 'generalized', 'function', 'generalized', 'probability', 'board', 'distribution', 'distribution', 'distribution', 'series', 'distribution', 'selection', 'distribution', 'function', 'function', 'distribution', 'constant', 'distribution', 'regularized')
t	('uniform', 'normal', 'done', 'similar', 'equal', 's', 'bessel', 'confidence', 'paired', 'special', 'student', 'owen', 'owen', 'classes', 'student')
though	('slightly', 'well-studied', 'equivalent', 'studied', 'intensity', 'connected', 'fundamentally', 'stationarity', 'been', 'mpp', 'care', 'stationary', 'several')
well-studied	('though',)
widespread	('consistent', 'inconsistent')
inconsistent	('widespread', 'ambiguous')
ambiguous	('inconsistent', 'square')
naturally	('deviation', 'mathematical', 'extended', 'get', 'distribution', 'processes')
assumption	('variate', 'basic', 'information', 'probability', 'implicit', 'distribution', 'under', 'hypotheses', 'under', 'true', 'paired', 'underlying', 'approximation')
producing	('value', 'confidence', 'value', 'best-fit')
ci	('interval', 'denoted', 'find', 'error', 'confidence', 'interval', 'sample')
control	('process', 'duncan', 'quality')
duncan	('control',)
romanovsky	('pp', 'oeis', ';', 'pearson')
a088802	(';',)
;	('a088802', 'romanovsky', 'time', 'simple', 'a014088', 'diaconis', 'a114598', 'mantel', 'spp', 'denotes', 'deviation', 'abramowitz', 'a093601', 'top', 'a086231', 'borwein', 'a060818', 'abramowitz', 'a034165', 'counting', 'index', 'macmahon', 'a086268', 'ziff', 'a092678', 'kenney', 'a092678', 'kenney', 'a046161', 'abramowitz')
appear	('two', 'he', 'plus', 'a001146', 'conjectured', 'present', 'kenney', 'independent')
reference	('no', 'normal', 'slovin', 'reportedly', 'without', 'particular', 'indicate')
implicitly	('quantity',)
whereas	('variance', 'continuous', 'interval', 'discrete', 'observed', 'usual', 'computation')
interpreting	('care', 'range', 'binary', 'constant', 'binary')
loosely	('very', 'knowing')
uncorrected	('variance',)
turns	('bias', 'out', 'first', 'up')
transformation	('linear', 'multiple', 'muller', 'correlation', 'muller', 'continuous', 'logit', 'logit', 'random', 'muller', 'cliff', 'differential', 'extra', 'muller', 'central', 'logit', 'normal', 'range', 'fisher', 'limit')
sigma	('distribution', 'standard', 'wolfram', 'generated', 'wolfram', 'generated', 'generated', 'sample', 'algebra', 'levy', 'distribution', 'th', 'standard')
whittaker	('pp', 'robinson', 'established', 'robinson')
robinson	('whittaker', 'whittaker')
multivariatestatistics`	('marginal', 'matrix', 'wishart', 'dimensionality', 'distribution')
marginal	('multivariatestatistics`', 'denoted', 'probability', 'probability', 'probability', 'probability', 'function', 'distribution', 'function', 'distribution')
independently	('normally', 'distributed', 'frucher', 'yamane', 'occur', 'first', 'uniformly', 'distributed', 'element', 'distributed', 'fitting', 'derived', 'matrix', 'moore', 'log', 'generally', 'distributed', 'two', 'distributed')
themselves	('variate', 'normally', 'fire', 'one', 'event', 'spaced')
joint	('matrix', 'probability', 'gaussian', 'variable', 'estimate', 'density', 'integer', 'function', 'distribution', 'function', 'distribution', 'subset', 'nonstationary', 'probability', 'entropy', 'gaussian', 'variable', 'gaussian', 'variable', 'respectively', 'probability', 'constant', 'distribution', 'discrete', 'distribution', 'distribution', 'variable', 'probability', 'form', 'distribution', 'distribution', 'probability')
expanding	('inverted', 'writing', 'term', 'edgeworth', 'collecting', 'large', 'value', 'logarithm')
solving	('written', 'defining', 'value', 'equation', 'rearranging', 'plugging', 'same', 'number', 'verified', 'line', 'best-fit', 'lie', 'fitting', 'plot', 'arise', 'best-fit', 'definition', 'simultaneously')
qed	('characteristic', 'markov')
bring	('rearranging', 'exponential')
braces	('term',)
sine	('over', 'term')
vanishes	('left', 'mode', 'th')
gaussian	('left', 'distribution', 'joint', 'spectrum', 'real', 'increment', 'mean', 'technique', 'noisy', 'polygon', 'function', 'difference', 'distribution', 'joint', 'variate', 'joint', 'product', 'ratio', 'sum', 'vector', 'multivariate-distributed', 'inverse', 'inverse', 'distribution', 'inverse', 'distribution', 'physicists', 'distribution', 'term', 'board', 'function', 'inverse', 'distribution', 'problem', 'integral', 'inverse', 'distribution', 'transform', 'transform', 'lindeberg')
explicit	('obtain', 'form', 'function', 'formula', 'outlier', 'labels')
singular	('function', 'case')
quadrant	('distribution', 'probability', 'variance', 'probability')
analytically	('case', 'rose', 'case', 'rose', 'evaluated', 'writing', 'evaluated', 'writing', 'square', 'moment', 'first', 'first', 'moment', 'singly', 'noncentral', 'first', 'moment', 'first', 'moment', 'first', 'moment', 'moment', 'euler-mascheroni')
stuart	('smith', 'ord', 'smith', 'ord')
ord	('stuart', 'rose', 'stuart', 'rose')
muller	('box', 'transformation', 'box', 'transformation', 'box', 'transformation', 'box', 'transformation')
price	('distribution', 'theorem', 'index', 'per', 'index', 'per', 'consumer', 'based', 'number', 'per', 'index', 'per', 'index', 'per', 'index', 'per', 'index', 'per', 'index', 'per', 'satisfies', 'theorem')
trivariate	('theorem', 'normal', 'distribution', 'normal', 'standardized', 'normal', 'p', 'normal')
cluster	('analysis', 'function', 'analysis', 'clusters', 'runs', 'analysis', 'adjust', 'radii', 'suspect', 'analysis', 'statistic', 'statistic', 'analysis', 'process', 'single', 'independent', 'viewed', 'tree', 'tree', 'perimeter', 'value', 'mean', 'count', 'mean', 'et')
classification	('technique', 'data', 'data')
partitioned	('elements', 'disjoint')
clusters	('group', 'represent', 'feature', 'cluster')
represent	('clusters', 'time', 'entries', 'number', 'table', 'equal', 'x')
proximate	('elements', 'based')
dissimilarity	('distance',)
pilot	('season',)
dark	('episode',)
matter	('television', 'even', 'no', 'many')
feature	('numb3rs', 'clusters')
math	('analysis', 'genius', 'articles', 'one', 'none', 'four')
genius	('math', 'charlie')
seemed	('student', 'systematically')
systematically	('seemed', 'singled')
singled	('systematically', 'out')
shooter	('season', 'fired', 'common', 'chance')
black	('season',)
charles	('character', 'eppes')
amita	('eppes', 'ramanujan')
ramanujan	('amita', 'adjust')
adjust	('ramanujan', 'cluster')
radii	('cluster', 'attempt')
attempt	('radii', 'time', 'been', 'book', 'refute', 'experts')
overlapping	('analysis', 'voronoi')
voronoi	('overlapping',)
movements	('track',)
suspect	('cluster',)
findclusters	('multivariate',)
hawkes	('processes', 'processes', 'univariate', 'process', 'upon', 'himself', 'linear', 'authors', 'processes', 'linear', 'processes', 'univariate', 'intensity-based', 'process', 'still', 'univariate', 'process', 'term', 'process', 'multivariate', 'multivariate', 'process', 'multivariate', 'processes', 'multivariate', 'processes', 'et', 'process', 'analysis', 'process', 'analysis', 'process', 'analysis', 'process', 'poisson', 'analysis', 'process')
notions	('many', 'distinct', 'intensity')
self-exciting	('temporal', 'univariate', 'temporal', 'process', 'denotes', 'process', 'occurrence')
temporal	('self-exciting', 'point', 'self-exciting', 'point', 'process', 'point', 'stochastic', 'point', 'intensity', 'point', 'process', 'point', 'spatial', 'point', 'process', 'point', 'spatial', 'point', 'process', 'point', 'spatial', 'point', 'process', 'point', 'spatial', 'point', 'process', 'point', 'spatial', 'point', 'process', 'point', 'spatial', 'point', 'process', 'point', 'spatial', 'point', 'process', 'point', 'point', 'view', 'point', 'viewing', 'point', 'viewing', 'point', 'simple', 'point', 'example', 'point', 'processes', 'point', 'spatial', 'point')
intensity	('conditional', 'conditional', 'function', 'conditional', 'function', 'conditional', 'stochastic', 'form', 'initial', 'time', 'process', 'time', 'process', 'inhomogeneous', 'process', 'conditional', 'whenever', 'function', 'conditional', 'function', 'conditional', 'temporal', 'conditional', 'function', 'notions', 'function', 'literature', 'point', 'though', 'function', 'function', 'density', 'pawlas', 'function', 'conditional', 'function', 'function', 'measure', 'measure', 'notion', 'measure', 'notion', 'pawlas', 'measure', 'conditional', 'function', 'function', 'function', 'definition', 'conditional', 'process')
background	('function', 'rate')
rate	('background', 'process', 'exponential', 'process', 'set', 'infinitesimal', 'failure', 'probability', 'hazard', 'force', 'hazard', 'probability', 'performed', 'distance', 'distribution', 'change', 'distribution', 'change', 'distribution', 'change', 'term')
governs	('function', 'clustering')
clustering	('governs', 'density', 'observed', 'galaxies')
exciting	('function', 'function', 'different', 'self', 'point', 'function', 'self', 'point', 'self', 'point', 'self', 'point', 'self', 'point', 'self', 'point', 'self', 'point', 'self', 'point', 'self', 'point')
excitation	('function', 'function', 'process', 'function')
merhdad	('authors', 'zhu', 'non-linear', 'zhu', 'authors', 'zhu', 'process', 'zhu')
zhu	('merhdad', 'conditional', 'merhdad', 'still', 'merhdad', 'generalized', 'merhdad', 'extended')
upon	('processes', 'hawkes', 'upwards', 'landing', 'agreed', 'avoid')
himself	('hawkes', 'most')
progress	('most', 'univariate')
behavior	('general', 'typically', 'occurred', 'asymptotic', 'probability', 'asymptotic', 'asymptotic', 'distribution')
typically	('behavior', 'most', 'describing', 'process', 'modeled', 'alternative', 'same', 'equivalent', 'other', 'measure', 'association')
differentiated	('processes', 'non-linear')
non-linear	('differentiated', 'counterparts', 'function', 'merhdad')
counterparts	('non-linear', 'conditional')
alternative	('two', 'brands', 'test', 'paired', 'nonparametric', 'paired', 'relatively', 'equal', 'use', 'definition', 'asked', 'typically', 'hypothesis', 'hypothesis', 'superposed', 'hypothesis', 'hypothesis', 'test', 'hypothesis', 'chance', 'out', 'hypothesis', 'value', 'hypothesis', 'effect', 'test', 'hypothesis', 'hypothesis', 'hypothesis', 'test', 'hypothesis', 'hypothesis', 'hypothesis')
brands	('alternative', 'univariate')
intensity-based	('one', 'hawkes', 'case', 'process')
cluster-based	('other', 'equivalent', 'version', 'difference', 'set')
studied	('though', 'different')
contexts	('different', 'dassios')
dassios	('contexts', 'zhao', 'structure', 'zhao')
zhao	('dassios', 'dassios', 'satisfies')
history	('form', 'process', 'time', 'limit', 'over')
adapted	('constant', 'time-dependent', 'dependent', 'processes')
self-excited	('size', 'jumps')
jumps	('self-excited', 'viewed', 'described')
viewed	('jumps', 'version', 'cluster', 'random')
immigrants	('elements', 'distributed', 'mark', 'independent', 'independent', 'distributed')
inhomogeneous	('distributed', 'poisson', 'processes', 'poisson', 'intensity', 'poisson')
immigrant	('distribution', 'function', 'process', 'time')
subject	('set', 'certain', 'anything', 'weighting', 'our', 'one', 'particular', 'seen', 'taken', 'set', 'model', 'presented', 'explanatory')
branching	('certain', 'structure')
structure	('branching', 'dassios', 'cliff', 'concentration', 'unexpected', 'indicating', 'triple', 'present')
ambiguities	('several',)
generalized	('zhu', 'polygon', 'become', 'rearranging', 'important', 'probability', 'probability', 'set', 'truncating', 'function', 'laguerre', 'easily', 'best-fit', 'moore-penrose', 'matrix', 'variously', 'obviously', 'multiple', 'parameter', 'exponential', 'function', 'laguerre', 'been', 'yield', 'involves', 'hypergeometric', 'function', 'hypergeometric', 'function', 'harmonic', 'distribution', 'sense', 'function', 'function')
includes	('example', 'adapting', 'kenney', 'chi-squared', 'voit')
adapting	('includes', 'process')
non-explosive	('collection', 'simple')
context	('function', 'sequence', 'moore-smith')
generation	('th', 'offspring', 'coin', 'random')
offspring	('generation', 'process')
classical	('reduces', 'linear', 'tosses', 'theory', 'connects', 'quantum', 'calculus', 'quantum', 'reduces', 'stochastic')
vast	('due', 'usage')
usage	('vast', 'term', 'word', 'roughly', 'particular', 'heartbeat')
among	('process', 'univariate', 'indices', 'those', 'p', 'amazing', 'over')
room	('expect', 'equally')
surprisingly	('most', 'treatment', 'simple', 'most')
assigned	('term', 'relatively', 'opening', 'one', 'probability', 'event')
relatively	('assigned', 'straightforward', 'alternative', 'knowledge', 'statistic', 'small')
extension	('straightforward',)
whenever	('process', 'intensity', 'stationary', 'stationary', 'constant', 'time')
bacry	('form', 'et')
stands	('et',)
generated	('sigma', 'up', 'sigma', 'over', 'sigma', 'over', 'number', 'random', 'point', 'highly', 'number', 'variable', 'uniformly', 'random', 'value', 'using', 'distribution', 'artificially', 'data')
distinguish	('authors', 'different', 'pseudo-', 'type')
liniger	('processes', 'other')
separate	('completely', 'segmented')
carlsson	('processes', 'et')
self	('probability', 'exciting', 'process', 'correcting', 'process', 'exciting', 'process', 'correcting', 'process', 'exciting', 'point', 'correcting', 'process', 'exciting', 'probable', 'exciting', 'process', 'correcting', 'process', 'correcting', 'process', 'exciting', 'process', 'correcting', 'process', 'exciting', 'process', 'correcting', 'process', 'exciting', 'process', 'correcting', 'process', 'exciting', 'dimensional', 'avoiding', 'walk', 'avoiding', 'dimensional', 'avoiding', 'a034166', 'avoiding', 'walk', 'avoiding', 'polygon', 'avoiding', 'conjectured', 'avoiding', 'walk', 'avoiding', 'coefficient', 'recursion')
multinormal	('distribution', 'distribution', 'matrix')
exist	('correlation', 'term', 'denotes', 'stationarity', 'general', 'correlation', 'matrix', 'believed', 'believed', 'seen', 'data', 'approximate', 'variable', 'two', 'raw', 'moment', 'derivative', 'probability')
adjective	('term', 'mean')
multivariable	('distribution', 'calculus')
calculus	('multivariable', 'multivariate', 'stochastic', 'stochastic', 'stochastic', 'classical', 'stochastic', 'random')
orthogonal	('multivariate',)
resultant	('multivariate', 'multivariate')
x2	('wolfram',)
nonzero	('case', 'thickness')
closed-form	('no', 'solution')
numerically	('multivariate', 'inverted', 'oeis', 'computed', 'computed')
composed	('matrix', 'row', 'grid', 'trajectories', 'self-similar', 'end', 'only')
wishart	('matrix', 'distribution', 'parameter', 'distribution', 'sample', 'distribution', 'multivariatestatistics`', 'distribution', 'matrix', 'hotelling', 'distribution')
freedom	('degree', 'parameter', 'population', 'within', 'calculate', 'table', 'degree', 'distribution', 'distribution', 'distributed', 'probability', 'degree', 'gamma', 'first', 'statistic', 'degree', 'hotelling', 'hotelling', 'degree', 'random', 'degree', 'degree', 'raw', 'degree', 'wolfram', 'gamma', 'degree', 'beyer', 'degree', 'smaller', 'student', 'distributed', 'independent')
describing	('typically', 'covariance', 'technique', 'bivariate', 'distribution', 'resonance', 'function', 'distribution', 'function', 'probability', 'function', 'cumulative')
f	('distribution', 'distribution', 'distribution', 'distribution', 'denoted', 'distribution', 'noncentral', 'distribution', 'distribution', 'ratio', 'distribution', 'distribution', 'distribution', 'distribution', 'noncentral', 'distribution', 'distribution', 'distribution', 'snedecor', 'distribution')
hotelling	('distribution', 't2', 'test', 'test', 't2', 'function', 't2', 'freedom', 'distribution', 'freedom', 'distribution', 'distribution', 'wishart')
t2	('hotelling', 'distribution', 'hotelling', 'distribution', 'hotelling', 'distribution')
bootstrap	('method', 'varian', 'non-normal', 'percolation', 'percolation')
computer-based	('method', 'method')
assigning	('method',)
efron	('estimate', 'tibshirani')
tibshirani	('efron', 'technique')
varian	('method', 'bootstrap')
generally	('method', 'superior', 'shuffle', 'properties', 'worsen', 'independently', 'normally')
superior	('generally',)
anova	('small', 'test', 'jackknife', 'regression', 'correlation', 'test', 'variance', 'level', 'restricting', 'group', 'statistical', 'number', 'balanced', 'statistical', 'test', 'univariate', 'test', 'test', 'bonferroni', 'analysis', 'arithmetic')
non-normal	('bootstrap',)
jackknife	('anova', 'permutation')
permutation	('jackknife', 'frequent', 'even', 'identity', 'original', 'continuous', 'two', 'distribution', 'distribution', 'run', 'paired')
resampling	('test',)
nonparametric	('robust', 'test', 'regression', 'technique', 'estimation', 'procedure', 'estimation', 'type', 'observation', 'estimation', 'test', 'formula', 'statistic', 'rho', 'alternative')
paired	('alternative', 'test', 'difference', 'take', 'alternative', 'difference', 'take', 'testing', 'parametric', 'value', 'permutation', 'two', 'value', 'determines', 'assumption', 'differ', 't', 'test', 'ratio', 'parametric', 'student', 'student')
signs	('only',)
getting	('probability', 'many', 'probability', 'least', 'probability', 'actual', 'probability', 'positive')
sign	('fisher', 'test', 'fisher', 'test', 'take', 'fisher', 'test', 'number', 'taken', 'fisher', 'test', 'fisher', 'test', 'fisher', 'test', 'correcting', 'error')
hypothesis	('test', 'testing', 'test', 'testing', 'value', 'testing', 'interval', 'testing', 'alternative', 'alternative', 'taken', 'alternative', 'statistical', 'test', 'test', 'testing', 'null', 'value', 'testing', 'proposition', 'statistic', 'statistical', 'refers', 'statement', 'alternative', 'symbolic', 'logic', 'first', 'conjecture', 'statistical', 'alternative', 'bourget', 'bourget', 'chinese', 'chinese', 'conjecture', 'continuum', 'continuum', 'testing', 'nested', 'null', 'null', 'postulate', 'riemann', 'schinzel', 'schinzel', 'souslin', 'souslin', 'testing', 'probability', 'process', 'testing', 'compare', 'null', 'ruled', 'alternative', 'valid', 'testing', 'alternative', 'bonferroni', 'test', 'null', 'null', 'p', 'distribution', 'assess', 'under', 'set', 'nested', 'nested', 'within', 'nested', 'statistical', 'null', 'statistical', 'tested', 'fisher', 'contrary', 'null', 'null', 'statistical', 'alternative', 'alternative', 'alternative', 'testing', 'test', 'testing', 'statistical', 'statistical', 'alternative', 'alternative', 'alternative', 'testing', 'null', 'false', 'false', 'false', 'less', 'false', 'accepted', 'type', 'null', 'sensitivity', 'true', 'rejected', 'type', 'null', 'sensitivity')
loess	('local', 'advance', 'local')
functional	('relationship', 'form', 'method', 'form', 'flexible', 'form', 'brownian', 'fact', 'relationship', 'fit', 'form', 'other', 'approximation', 'same', 'form')
advance	('loess', 'grid', 'fine')
absence	('data', 'guidance')
guidance	('absence', 'constraints')
constraints	('guidance',)
meaningful	('no', 'statistically', 'results')
artificial	('technique', 'neural', 'estimation', 'neural')
neural	('artificial', 'networks', 'artificial', 'networks')
networks	('neural', 'kernel', 'neural', 'model')
kernel	('networks', 'gradients', 'estimation', 'function', 'assign')
expressing	('function', 'weighted', 'formula', 'matrix', 'theorem', 'idea')
sigmoids	('logit',)
logit	('sigmoids', 'applying', 'transformation', 'distribution', 'transformation', 'conditional', 'regression', 'conditional', 'regression', 'regression', 'test', 'transformation')
relevant	('function', 'explanatory', 'trial', 'biology', 'matrix', 'gamma')
explanatory	('relevant', 'subject')
flexible	('extremely', 'functional')
nonlinear	('estimation', 'least-squares', 'legendre', 'least', 'linearize', 'function', 'parameter', 'fit', 'inverse', 'least', 'regression', 'least', 'analysis', 'least', 'example', 'least', 'before', 'least', 'inverse', 'least', 'regression', 'least')
least-squares	('nonlinear', 'iterative')
iterative	('least-squares', 'search', 'resorting')
search	('iterative', 'algorithm')
gradients	('kernel',)
specifies	('estimation', 'conditional')
parametric	('no', 'form', 'paired', 'test', 'data', 'test', 'paired', 'test')
whatsoever	('density',)
seeing	('estimated', 'what', 'probability', 'before', 'before', 'less')
involves	('procedure', 'use', 'messy', 'generalized')
assign	('kernel', 'weights', 'marking', 'probability', 'probability', 'single')
weights	('assign', 'nearby', 'scheme', 'sum')
nearby	('weights',)
reorder	('variate', 'th')
somtimes	('formula', 'spelled')
spelled	('somtimes', 'forumula', 'ito', 'ito')
forumula	('spelled', 'altares')
altares	('forumula', 'et')
ad	('p', 'hoc')
hoc	('ad', 'formula')
lacking	('formula', 'mathematical')
rigor	('mathematical', 'ryan')
ryan	('rigor', 'estimate', 'variability', 'slovin')
allowed	('size', 'probability', 'air', 'restrictions', 'directions', 'only', 'discrete', 'parameter', 'vary')
supposedly	('formula', 'published')
published	('supposedly', 'slovin', 'distribution', 'william')
slovin	('published', 'reference', 'property', 'formula', 'ryan', 'formula', 'variance', 'formula')
reportedly	('reference', 'guilford')
guilford	('reportedly', 'frucher')
frucher	('guilford', 'independently')
yamane	('independently', 'unclear')
unclear	('yamane', 'useful')
imprecise	('only', 'definition')
variability	('population', 'measured', 'representing', 'ryan')
lacks	('formula', 'parameter')
representing	('parameter', 'variability', 'binary', 'dimension')
spearman	('rank', 'coefficient', 'proposed', 'measure', "d'abrera", 'rank', 'misleading', 'rank', 'rank', 'rank', 'variance', 'rank', 'estimate', 'rank', 'test', 'rank', 'coefficient', 'rank', 'fisher', 'rank')
rho	('nonparametric', 'th')
distribution-free	('rank',)
associations	('strength', 'two')
lehmann	('variable', "d'abrera")
d'abrera	('lehmann', 'spearman')
r-estimate	('measure', 'wilcoxon', 'kolmogorov')
monotone	('measure', 'association', 'function', 'increasing')
association	('monotone', 'distribution', 'two', 'typically', 'contingency', 'significant', 'journal')
make	('data', 'pearson', 'pepys', 'data', 'smooth')
undesirable	('coefficient',)
misleading	('spearman', 'game', 'payoff')
higher-order	('excess', 'second-')
assumes	('test', 'information', 'variate', 'element', 'variate', 'value', 'regression', 'model', 'distribution', 'value', 'variate', 'value', 'variate', 'value', 'variate', 'value')
magnitudes	('information',)
add	('value',)
p-value	('statistic', 'equal', 'point', 'alpha', 'test', 'probability', 'type')
wilcoxon	('table', 'test', 'r-estimate', 'signed', 'test', 'test', 'test', 'signed', 'test', 'signed', 'coefficient', 'rank', 'test', 'signed', 'error', 'signed', 'student', 'signed', 'error', 'rank', 'test', 'signed')
axioms	('probability', 'kolmogorov', 'state', 'kolmogorov', 'probability', 'probability', 'probability', 'sample', 'probability', 'probability')
bayes	('pp', 'theorem', 'probability', 'theorem', 'probability', 'theorem', 'probability', 'theorem', 'probability', 'theorem')
inclusion	('probability', 'exclusion', 'set', 'exclusion', 'because', 'irrelevant', 'probability', 'exclusion')
exclusion	('inclusion', 'principle', 'inclusion', 'principle', 'inclusion', 'principle')
principle	('exclusion', 'independent', 'slightly', 'exclusion', 'odd', 'insufficient', 'fermat', 'conjunctive', 'fermat', 'conjunctive', 'patrons', 'casinos', 'multiplication', 'probability', 'first', 'pp', 'pp', 'opposed', 'devoted', 'refute', 'poincare', 'poincare', 'insufficient', 'exclusion', 'mutually', 'number', 'insufficient', 'number', 'insufficient')
matching	('group', 'birthdays', 'asymptotically', 'underlying')
birthdays	('matching', 'out', 'start', 'distribution', 'assumed', 'share', 'smallest', 'coincident', 'oeis')
start	('birthdays', 'arbitrary', 'out', 'following', 'motion', 'one', 'brownian', 'grid', 'end', 'sequence', 'single')
birthday	('probability', 'person', 'different', 'person', 'different', 'probability', 'shared', 'probability', 'shared', 'a050256', 'two', 'within', 'mosteller', 'problem', 'probability', 'attack', 'probability', 'problem', 'probability', 'problem', 'probability', 'problem')
shared	('birthday', 'no', 'birthday', 'people')
relation	('finch', 'certain', 'operator', 'namely', 'well', 'recursion', 'raw', 'mean', 'mean', 'negative')
finch	('relation', 'time', 'flajolet', 'following', 'hanson', 'sequence', 'noonan', 'upper', 'disproven', 'renyi')
recursive	('time', 'function')
grows	('function', 'exponentially')
exponentially	('grows', 'rapidly', 'average', 'weighted', 'exponential')
rapidly	('exponentially',)
years	('unwieldy', 'been')
existence	('assumed', 'leap')
leap	('existence', 'days')
days	('leap', 'within', 'out')
ignored	('distribution', 'disappears')
year	('throughout', 'harmonic', 'event', 'united')
actuality	('increase',)
september	('average', 'united')
states;	('united', 'peterson')
peterson	('states;', 'number')
chance	('least', 'least', 'get', 'two', 'us', 'going', 'greatest', 'going', 'greater', 'player', 'mean', 'particular', 'game', 'one', 'shooter', 'dying', 'number', 'specified', 'amount', 'variation', 'alternative', 'component', 'concept', 'alpha', 'occurred', 'significance')
share	('two', 'birthdays')
a033810	('minimal',)
coincident	('least', 'birthdays')
a014088	(';',)
diaconis	(';', 'mosteller', 'function', 'mosteller', 'approximation', 'mosteller', "sevast'yanov", 'mosteller', 'paulos', 'et', 'landing', 'et', 'connection', 'mosteller', 'happen', 'mosteller', 'remarkable', 'mosteller')
mosteller	('diaconis', 'probability', 'diaconis', 'formula', 'diaconis', 'oeis', 'diaconis', 'birthday', 'diaconis', 'large', 'grünbaum', 'et', 'diaconis', 'littlewood', 'diaconis', 'law')
latter	('estimated', 'error', 'distribution', 'function', 'parameters;', 'view', 'viewing', 'former', 'function', 'simplifies')
sayrafiezadeh	('error', 'computed')
regularized	('formula', 'hypergeometric', 'dice', 'hypergeometric', 'function', 'beta', 'distribution', 'gamma', 'function', 'gamma', 'function', 'beta', 'distribution', 'beta', 'function', 'gamma', 'confluent', 'function', 'hypergeometric', 'function', 'beta', 'function', 'hypergeometric', 'function', 'beta')
a050255	('differ',)
differ	('a050255', 'true', 'probability', 'probability', 'trial', 'expected', 'determines', 'other', 'paired', 'mean', 'significantly')
poorer	('simpler', 'approximation')
a050256	('birthday',)
asks	('problem', 'number', 'problem', 'find', 'problem', 'find', 'problem', 'probability', 'problem', 'probability')
day	('within',)
abramson	('other', 'moser')
moser	('abramson', 'who')
suffice	('approximation',)
match	('two', 'within')
sevast'yanov	('possible', 'diaconis')
attack	('birthday', 'coincidence')
coincidence	('attack', 'small', 'surprising', 'possible--and', 'p', 'probability', 'trial', 'random', 'random', 'value', 'confidence', 'theorem', 'frivolous')
sultan	('problem', 'dowry')
dowry	('sultan', 'problem')
bonferroni	('true', 'inequalities', 'inequalities', 'probability', 'inequalities', 'correction', 'approach', 'form', 'inequalities', 'correction', 'hypothesis', 'correction', 'conservative', 'anova', 'correction')
boole	('inequality', 'inequality')
disjoint	('denotes', 'probability', 'partitioned')
beautiful	('equality', 'theorem', 'head', 'formula')
unions	('probability', 'probabilities')
inclusion-exclusion	('event',)
wider	('slightly', 'class')
inequalities	('class', 'bonferroni', 'bonferroni', 'probability', 'bonferroni', 'bonferroni', 'better', 'feller')
equivalently	('extreme', 'exponential', 'assumed', 'distribution')
none	('probability', 'science', 'math', 'even', 'original')
borel	('occur', 'cantelli', 'ieif', 'relative', 'process', 'p', 'tanner', 'form', 'element')
cantelli	('borel', 'lemma')
lemma	('cantelli', 'probability', 'ito', 'kiyoshi', 'ito', 'random', 'fekete', 'connective', 'ito', 'random', 'pearson', 'statistical')
buffon-laplace	('needle', 'line', 'needle', 'game', 'needle')
needle	('buffon-laplace', 'problem', 'probability', 'length', 'position', 'specified', 'probabilities', 'crossing', 'short', 'crosses', 'side', 'length', 'probability', 'contained', 'laplace', 'problem', 'buffon', 'problem', 'buffon', 'problem', 'probability', 'length', 'short', 'one', 'probability', 'long', 'one', 'distance', 'midpoint', 'formed', 'short', 'size', 'tosses', 'length', 'crossing', 'short', 'above', 'throwing', 'board', 'buffon-laplace', 'buffon', 'problem', 'laplace', 'problem', 'buffon-laplace', 'buffon', 'laplace', 'problem', 'buffon', 'problem', 'laplace', 'problem', 'buffon', 'problem')
length	('needle', 'land', 'needles', 'needles', 'needle', 'less', 'needle', 'land', 'needle', 'parameter', 'side', 'tile', 'edge', 'probability', 'side', 'radius', 'edge', 'probability', 'side', 'radius', 'edge', 'probability', 'side', 'radius', 'side', 'probability', 'tail', 'occur', 'subsequences', 'euler-mascheroni', 'depend', 'location', 'partitions', 'number', 'two', 'random', 'equal', 'taken', 'self-avoiding', 'wire', 'wires', 'oeis', 'paths', 'up', 'function', 'shortest', 'least', 'block', 'one', 'block', 'block', 'one', 'sequence', 'term', 'th', 'run', 'clumps', 'sequence', 'run', 'encoding', 'above', 'proportional', 'leg', 'eight', 'unit', 'parked')
land	('length', 'least', 'length', 'coin', 'partially', 'grid', 'grid', 'likely', 'side', 'coin', 'never', 'same')
grid	('floor', 'equally', 'consisting', 'square', 'hexagonal', 'hexagonal', 'composed', 'possible', 'land', 'land', 'buffon', 'tile', 'probability', 'tile', 'tile', 'advance', 'fine', 'obtain', 'square', 'lattice', 'nonnegative', 'nonnegative', 'walk', 'start', 'square', 'one')
spaced	('equally', 'equally', 'equally', 'parallel', 'themselves', 'discrete', 'bin', 'apart', 'collected', 'equal', 'evenly', 'nails')
apart	('position', 'problem', 'spaced', 'class')
orientation	('point', 'coordinate', 'use')
coordinate	('orientation', 'binary', 'order', 'vertical', 'best-fit')
rectangle	('single', 'using', 'height', 'number', 'function')
opposite	('addition', 'orientations', 'angles', 'pin', 'top', 'midpoint', 'centroid', 'probability')
orientations	('opposite',)
uspensky	('probability', 'pp', 'expression', 'badger', 'polygon', 'papoulis', 'defines', 'specifically', 'satisfies', 'kenney', 'satisfies', 'variance', 'shown', 'least', 'true', 'form')
solomon	('p', 'problem', 'mantel', 'p', 'blaisdell', 'dvoretzky')
solved	('first', 'buffon', 'who', 'problem', 'problem', 'closed', 'fit', 'premultiplying', 'equation', 'equation', 'using', 'cannot', 'moment-generating')
buffon	('solved', 'p', 'laplace', 'probability', 'needle', 'needle', 'naturalist', 'naturalist', 'solution', 'solution', 'estimator', 'estimator', 'problem', 'needle', 'probability', 'laplace', 'investigated', 'tiled', 'investigated', 'grid', 'needle', 'probability', 'laplace', 'problem', 'needle', 'plot', 'laplace', 'problem', 'needle')
derivation	('pp', 'contained', 'alternate', 'see')
crossing	('needle', 'tosses', 'asymptotic', 'needle', 'line')
tosses	('time', 'short', 'crossing', 'short', 'figure', 'needle', 'green', 'cross', 'series', 'million', 'trial', 'distribution', 'approximation', 'identical', 'occur', 'fibonacci', 'occur', 'fibonacci', 'number', 'possible', 'minimum', 'number', 'havil', 'number', 'get', 'classical', 'many', 'finally', 'number', 'win', 'independent', 'occur', 'fibonacci', 'win')
short	('tosses', 'needle', 'parameter', 'needle', 'tosses', 'needle', 'needle')
crosses	('needle', 'ball', 'bottom')
perlman	('parameter', 'wichura', 'variance', 'wishura', 'estimator', 'wishura')
wichura	('perlman', 'point')
uniformly	('estimator', 'minimum', 'estimator', 'minimum', 'distribution', 'independently', 'distribution', 'distributed', 'fills', 'uncorrelated', 'produce', 'distributed', 'distribution', 'distributed', 'normalization', 'distributed', 'generated', 'distributed', 'variate', 'volume', 'partitioning', 'angle', 'distributed', 'series', 'valid', 'sampled', 'interval', 'mathematicians', 'use', 'yield', 'distributed')
wishura	('perlman', 'estimator', 'perlman', 'variance')
asymptotic	('estimator', 'variance', 'crossing', 'variance', 'statistic', 'probability', 'fisher', 'expansion', 'kostlan', 'behavior', 'examine', 'behavior', 'behavior', 'expansion', 'expression', 'series', 'statistical', 'fisher', 'expansion', 'fisher', 'expansion', 'statistical', 'form', 'statistical', 'obtain', 'expansion', 'statistical', 'fisher', 'expansion', 'statistical', 'theorem', 'normalized', 'approximation', 'series', 'theorem', 'equipartition')
a114602	('set',)
needles	('above', 'length', 'length', 'intersecting')
intersecting	('needles', 'those', 'single', 'those', 'two')
green	('those', 'tosses')
yellow	('those', 'indicated', 'disks', 'uniform')
red	('plane', 'shown', 'those', 'indicated', 'value', 'curve', 'analogous')
plane	('red', 'tiled', 'spatial', 'fano', 'small', 'refers', 'diagram', 'tetrahedron', 'diagram', 'wigner', 'complex', 'trott', 'sum', 'bends', 'alm')
tiled	('plane', 'congruent', 'buffon')
congruent	('tiled', 'triangles')
triangles	('congruent', 'one', 'angles', 'simplifies')
shortest	('less', 'altitude', 'true', 'length')
altitude	('shortest',)
thrown	('probability', 'tile', 'coin', 'thickness', 'air', 'dice')
entirely	('contained', 'within', 'lie', 'single', 'lie', 'single', 'lie', 'single')
angles	('triangles', 'opposite')
triangle	('triangular', 'equilateral', 'insetting', 'insetting', 'side', 'insetting', 'side', 'padded', 'coefficient', 'papoulis', 'list', 'point', 'median', 'statistical', 'trapezoid', 'centroid', 'centroid', 'median', 'table', 'distribution', 'function')
equilateral	('consisting', 'side', 'triangle')
simplifies	('triangles', 'markoff', 'distribution', 'standard', 'defining', 'exponential', 'distribution', 'case', 'latter', 'expected', 'function', 'moment-generating')
clean	('problem', 'tile', 'problem', 'tile', 'tile', 'case', 'tile')
tile	('clean', 'problem', 'clean', 'problem', 'clean', 'game', 'thrown', 'length', 'greater', 'triangular', 'hexagonal', 'special', 'grid', 'edge', 'single', 'indicated', 'single', 'two', 'quantities', 'ratio', 'figure', 'fraction', 'fraction', 'covered', 'fraction', 'fraction', 'covered', 'grid', 'edge', 'single', 'shortening', 'single', 'two', 'quantities', 'grid', 'edge', 'single', 'shortening', 'single', 'two', 'quantities', 'single', 'probability', 'single', 'two', 'quantities', 'clean', 'problem')
posed	('first', 'french', 'he', 'question')
french	('posed', 'naturalist', 'dice', 'nobleman')
naturalist	('french', 'buffon', 'buffon')
reproduced	('pp', 'solution')
shorter	('one', 'distance')
a060294	('long',)
longer	('one', 'distance', 'odd', 'you', 'no', 'other')
intersects	('least',)
kunkel	('writing',)
midpoint	('needle', 'nearest', 'vertices', 'opposite', 'two')
angle	('line', 'formed', 'opening', 'insetting', 'critical', 'cylinder', 'arbitrary', 'uniformly', 'pass', 'definition', 'noisy', 'nine', 'normalized', 'general')
formed	('angle', 'needle', 'tiling', 'rhombi', 'shape', 'bending', 'yield', 'point')
place	('intersection', 'restricted', 'many', 'rotates', 'event', 'indication', 'abramowitz')
restricted	('place', 'horizontal', 'nonnegative', 'horizontal', 'nonnegative', 'only', 'take', 'observation', 'same', 'value')
asymptotically	('estimator', 'unbiased', 'likely', 'approaching', 'probabilities', 'matching', 'function', 'normally', 'sum')
a114598	(';',)
mantel	(';', 'solomon')
missing	('those', 'shown')
cross	('tosses', 'wire', 'right', 'coefficient', 'correlation', 'correlation')
experimentally	('been', 'confirmed', 'bartoš')
needle-tossing	('five',)
critical	('statistic', 'analysis', 'piñero', 'angle', 'finite', 'exponent', 'finite', 'exponent', 'test', 'experiment-wide', 'value', 'against', 'greater', 'comparison', 'value', 'region', 'best', 'region')
needle-tossings	('see',)
badger	('see', 'uspensky')
experiments	('pp', 'conducted')
conducted	('experiments',)
convex	('shape', 'regular', 'polytopes', 'amazingly', 'unfold', 'polyhedra')
diameter	('less', 'coin', 'square', 'coin', 'lie', 'coin', 'lie', 'coin', 'lie', 'coin', 'poured')
intersect	('one', 'paths', 'median', 'point')
perimeter	('polygon', 'cluster', 'lattice')
further	('p', 'generalization', 'complement', 'set', 'index', 'number')
throwing	('generalization', 'needle', 'probability', 'least')
board	('needle', 'ruled', 'galton', 'markov', 'galton', 'gaussian', 'galton', 'grains', 'size', 'galton', 'hypergeometric', 'quincunx', 'upright', 'evenly', 'variant', 'only', 'galton', 'discrete')
ruled	('board', 'two', 'hypothesis')
perpendicular	('set', 'minimized', 'based', 'vertical', 'measured', 'fitting', 'offsets', 'minimized', 'based', 'point', 'distance', 'square', 'fitting')
gambling	('game',)
game	('gambling', 'played', 'tile', 'investigated', 'case', 'buffon-laplace', 'disks', 'fair', 'two', 'fair', 'two', 'fair', 'two', 'fair', 'chance', 'first', 'version', 'player', 'modified', 'concluded', 'player', 'misleading')
played	('game', 'carnivals')
carnivals	('played', 'player')
player	('carnivals', 'bet', 'bet', 'betting', 'betting', 'betting', 'betting', 'finite', 'say', 'one', 'one', 'either', 'probability', 'one', 'two', 'one', 'pennies', 'starting', 'chance', 'starting', 'bernoulli', 'head', 'pays', 'wagered', 'still', 'game', 'receives', 'game', 'payoff', 'apparently', 'time', 'first', 'gain', 'whopping', 'amount')
bet	('player', 'one', 'player', 'number', 'chamber', 'only', 'many', '$2', 'shown', 'wagering', 'doubled')
rolled	('dice', 'number', 'least', 'least', 'pepys')
he	('appear', 'receives', 'stake', 'loses', 'should', 'posed', 'wager', 'planned', 'loaded', 'toss', 'lost', 'toss', 'wins', 'looked', 'developed', 'pseudonym', 'chose')
receives	('he', 'back', 'initially', 'dollars', 'player', 'nothing')
back	('receives', 'multiple', 'plugging', 'simplifying', 'plugging', 'simplifying')
stake	('original', 'equal', 'he', 'expected')
loses	('he',)
loss	('expected', 'per', 'halved', 'without')
per	('loss', 'roll', 'count', 'site', 'count', 'site', 'price', 'unit', 'price', 'unit', 'price', 'unit', 'price', 'unit', 'price', 'unit', 'price', 'unit', 'price', 'unit', 'price', 'unit')
roll	('per', 'chuck', 'single', 'wager', 'sixes', 'dice')
chuck	('roll', 'luck')
luck	('chuck', 'probability')
investigated	('game', 'buffon', 'buffon', 'probabilities')
coin	('thrown', 'partially', 'greater', 'diameter', 'possible', 'land', 'probability', 'diameter', 'radius', 'probability', 'probability', 'landing', 'probability', 'landing', 'probability', 'diameter', 'radius', 'probability', 'probability', 'diameter', 'radius', 'probability', 'probability', 'lie', 'flipping', 'probability', 'tossing', 'idealized', 'circular', 'probability', 'two-sided', 'distribution', 'flipping', 'introduces', 'causes', 'spend', 'introduced', 'slightly', 'fair', 'toss', 'total', 'flips', 'properties', 'fair', 'probability', 'finite', 'landing', 'diameter', 'fair', 'over', 'p', 'tossing', 'cards', 'dice', 'probability', 'tossing', 'before', 'dollars', 'probability', 'tossing', 'land', 'face', 'tossing', 'bernoulli', 'smallest', 'card', 'tossing', 'distribution', 'tossing', 'rolling', 'generation', 'tail', 'distribution', 'tossing', 'number', 'tossed', 'distribution', 'distribution', 'tossing')
partially	('coin', 'cover', 'land', 'covers')
cover	('partially', 'floor', 'glass', 'allow')
regularly	('floor',)
hexagonal	('grid', 'grid', 'tile', 'figure', 'alm', 'planar')
rhombi	('side', 'formed', 'opening')
covers	('partially',)
edge	('tile', 'length', 'tile', 'length', 'tile', 'length', 'been', 'landing', 'computed', 'joined', 'need', 'cut', 'funnel')
indicated	('tile', 'yellow', 'two', 'red', 'categories', 'using', 'outlier', 'separately')
disks	('yellow', 'game')
shortening	('figure', 'side', 'tile', 'side', 'tile', 'side')
insetting	('square', 'square', 'triangle', 'triangle', 'hexagon', 'triangle', 'angle', 'rhombus')
radius	('length', 'coin', 'length', 'coin', 'length', 'coin', 'cylinder', 'thickness', 'random', 'central', 'restitution')
fair	('game', 'two', 'game', 'two', 'game', 'two', 'game', 'two', 'probability', 'coin', 'example', 'coin', 'toss', 'coin', 'concluded', 'entrance', 'absolutely', 'gambler', 'absolutely', 'feller', 'absolutely', 'random', '◇', 'bit')
betting	('player', 'single', 'player', 'single', 'player', 'single', 'player', 'single')
landing	('probability', 'two', 'coin', 'three', 'coin', 'four', 'initial', 'diaconis', 'upon', 'confidence', 'thickness', 'coin', 'edge')
shaded	('ratio', 'area')
covered	('tile', 'region', 'tile', 'device', 'glass')
region	('covered', 'figure', 'critical', 'size', 'critical', 'size', 'closed', 'efficiently', 'extrema', 'rose', 'probability', 'computed')
disk	('figure', 'circular', 'zero', 'complex', 'complex', 'one', 'separated', 'center')
regular	('side', 'hexagon', 'net', 'convex')
hexagon	('regular', 'insetting')
quadrilateral	('equal',)
tiling	('formed', 'truchet')
opening	('rhombi', 'angle', 'assigned', 'funnel', 'dropped')
rhombus	('insetting', 'side')
flipping	('coin', 'probability', 'proposed', 'coin', 'papoulis')
tossing	('coin', 'penny', 'results', 'coin', 'probability', 'coin', 'martingale', 'coin', 'gambler', 'coin', 'de', 'coin', 'eulerian', 'coin', 'run', 'occurrence', 'example', 'coin', 'geometric', 'coin', 'random')
circular	('coin', 'disk', 'girko', 'law', 'girko', 'girko', 'law', 'girko', 'law', 'adjacent', 'wedges', 'chart', 'sector', 'distribution', 'analog', 'mean', 'variance')
thickness	('zero', 'thrown', 'nonzero', 'actual', 'finite', 'landing', 'radius', 'comprising', 'mm')
air	('thrown', 'allowed', 'time', 'before')
rest	('fall', 'either')
face	('side', 'up', 'chernoff', 'coin', 'median', 'using', 'chernoff', 'statistical')
two-sided	('coin',)
die	('despite', 'slightly', 'complexity')
despite	('die', 'slight', 'process', 'number', 'molchanov', 'number', 'moreover', 'looking')
spinning	('penny',)
penny	('spinning', 'tossing', 'transfer', 'loser')
paulos	('time', 'diaconis')
introduces	('coin', 'small')
wobble	('degree', 'causes')
causes	('wobble', 'coin', 'cylinder')
spend	('coin', 'time')
facing	('side', 'initially', 'upward', 'side', 'upwards')
initially	('side', 'facing', 'receives')
upward	('facing', 'before')
toss	('before', 'top', 'coin', 'opposed', 'twice', 'number', 'fair', 'minimal', 'expectation', 'he', 'he', 'th', 'seen', 'space', 'two')
prediction	('observation', 'been', 'value', 'theory', 'periodogram', 'theory')
confirmed	('been', 'experimentally')
bartoš	('experimentally', 'et', 'interval', 'et')
collected	('who', 'total', 'data', 'spaced')
flips	('coin', 'probability')
upwards	('facing', 'upon')
trace	('no', 'heads-tails', 'matrix')
heads-tails	('trace',)
counterintuitive	('et', 'properties')
properties	('counterintuitive', 'coin', 'artifice', 'distribution', 'following', 'invariance', 'including', 'vacuum', 'mathematical', 'vary', 'uncertainties', 'convergence', 'generally', 'investigating', 'underlying', 'estimator', 'underlying', 'estimate', 'underlying', 'random', 'amazing', 'normal', 'physical', 'statistical', 'real')
twice	('toss', 'likely', 'point', 'outer')
triple	('likely', 'specified', 'measurable', 'domain', 'structure', 'watson', 'watson')
tth	('encountered',)
tht	('three',)
thh	('precede',)
precede	('thh',)
furthermore	('six',)
htt	('first',)
ttt	('occur',)
honsberger	('other', 'strings')
strings	('honsberger',)
wait	('expected', 'see', 'expected', 'see')
string	('see', 'less', 'long', 'random', 'produce', 'random')
gardner	('less', 'berlekamp', 'hthh', 'probability', 'penney', 'probability', 'assertion', 'almost')
berlekamp	('gardner', 'et')
hthh	('probability', 'gardner')
thth	('before',)
tthh	('before',)
hhh	('probability', 'penney')
thhh	('before',)
penney	('hhh', 'gardner')
hernández-navarro	('computed', 'piñero')
piñero	('hernández-navarro', 'critical')
cylinder	('angle', 'radius', 'round', 'causes', 'imbalance', 'tend')
comprising	('thickness',)
remarkably	('expression',)
us	('chance', 'tells', 'fekete')
mm	('thickness',)
quarter	('study',)
well-developed	('detailed',)
detailed	('well-developed', 'treatment', 'out', 'historically', 'historically', 'analysis')
treatment	('detailed', 'surprisingly', 'level', 'error', 'level')
nature	('simple', 'underlying', 'discrete', 'distribution')
consecutive	('two', 'no', 'two', 'one', 'identical', 'run', 'no', 'group', 'ignoring')
fibonacci	('tosses', 'tosses', 'random', 'random', 'sequence', 'sequence', 'tosses')
subsequences	('occur', 'get', 'length', 'mean')
a052944	('minimal',)
ht	('sequence',)
a001146	('appear',)
cards	('trial', 'coin', 'deck', 'successively', 'exchanging', 'position', 'position', 'randomly', 'identity', 'before', 'repeated', 'interchanging', 'position', 'position', 'randomly', 'layers', 'randomizes', 'keller', 'shuffle', 'exchange')
gambler	('dice', 'ruin', 'nobleman', 'chevalier', 'quicker', 'ruin', 'tossing', 'ruin', 'dice', 'ruin', 'fair', 'ruin')
ruin	('gambler', 'martingale', 'gambler', 'probability', 'gambler', 'geometric', 'gambler', 'index', 'gambler', 'random')
martingale	('ruin', 'run', 'tossing', 'saint', 'distribution', 'due', 'example', 'random', 'walk', 'chain', 'percolation')
run	('martingale', 'saint', 'common', 'long', 'plot', 'sharing', 'over', 'sequence', 'sequence', 'probability', 'consecutive', 'constant', 'longest', 'expected', 'gordon', 'length', 'probability', 'variance', 'permutation', 'language', 'length', 'look', 'sequence', 'connected', 'satisfies', 'mean', 'count', 'mean', 'density', 'theory', 'percolation', 'tossing', 'distribution')
saint	('run', 'petersburg', 'martingale', 'petersburg', 'distribution', 'petersburg', 'dimensional', 'petersburg', 'win', 'petersburg', 'distribution', 'petersburg')
petersburg	('saint', 'paradox', 'saint', 'paradox', 'saint', 'paradox', 'saint', 'paradox', 'saint', 'saint', 'paradox')
paradox	('petersburg', 'petersburg', 'end', 'clearly', 'petersburg', 'probability', 'amalgamation', 'reversal', 'yule-simpson', 'effect', 'statistical', 'simpson', 'arise', 'simpson', 'probability', 'petersburg', 'formula', 'petersburg')
surprising	('coincidence', 'concurrence', 'due', 'central', 'close')
concurrence	('surprising',)
perceived	('event', 'meaningfully')
meaningfully	('perceived', 'no')
apparent	('no', 'causal', 'number', 'number')
causal	('apparent', 'connection', 'arise')
unlikely	('extremely',)
possible--and	('coincidence', 'perhaps')
perhaps	('possible--and', 'even')
quote	('common', 'sherlock')
sherlock	('quote', 'holmes')
holmes	('sherlock', 'adventure')
adventure	('holmes', 'blue')
blue	('adventure', 'action', 'reaction', 'moving', 'normal')
action	('blue',)
reaction	('blue', 'dense')
dense	('reaction', 'swarm')
swarm	('dense',)
humanity	('possible',)
combination	('possible', 'two', 'hermite', 'actual')
conan	('striking', 'doyle')
doyle	('conan',)
truly	('law', 'large', 'become', 'number', 'law', 'large', 'law', 'large', 'law', 'large')
insufficient	('principle', 'reason', 'principle', 'reason', 'principle', 'reason', 'principle', 'reason')
infinitesimal	('rate',)
algebraically	('provided',)
provided	('algebraically', 'quantity', 'process', 'density')
strictly	('time', 'prior', 'value', 'p', 'continuous', 'sequence', 'variable', 'value')
occurred	('denoted', 'already', 'yield', 'relationship', 'event', 'altogether', 'behavior', 'could', 'chance')
venn	('using',)
multiplying	('diagram', 'half-plane', 'expected', 'normalizing', 'oeis')
fermat	('theorem', 'principle', 'happened', 'principle')
conjunctive	('principle', 'probability', 'principle', 'probability', 'probability')
picked	('objects', 'repeatedly', 'object', 'been', 'least', 'people', 'random', 'number', 'random')
repeatedly	('picked', 'probability')
object	('probability', 'picked', 'statistical', 'inverse', 'complex', 'replacement', 'without', 'one', 'number', 'type', 'mathematical', 'consisting', 'originally')
try	('find',)
earliest	('find', 'time')
once	('coupon', 'data')
coupon	('once', 'collector')
collector	('coupon', 'problem')
double-six	('one', 'throws', 'one', 'de')
nobleman	('french', 'gambler')
chevalier	('gambler', 'de')
de	('chevalier', 'mere', 'problem', 'mere', 'fact', 'mere', 'double-six', 'mere', 'probability', 'mere', 'tossing', 'mere', 'defines', 'moivre-laplace', 'pp', 'moivre', 'feller', 'moivre', 'binomial', 'moivre')
mere	('de', 'suspected', 'de', 'de', 'observation', 'de', 'problem', 'de', 'problem', 'de', 'problem')
suspected	('mere', 'higher')
skills	('mathematical', 'great')
great	('skills', 'enough', 'out', 'still', 'deal', 'probability', 'observed', 'least', 'probable')
enough	('great', 'demonstrate', 'evans', 'large')
demonstrate	('enough', 'why')
why	('demonstrate', 'should')
question	('posed', 'plouffe', 'number')
pascal	('who', 'fact', 'distribution', 'distribution')
boxcars	('probability', 'dice')
newton	('dice', 'pepys', 'isaac', 'long', 'likely', 'correctly', 'probability', 'conclusion', 'inspection', 'pepys')
pepys	('newton', 'problem', 'samuel', 'wrote', 'make', 'asked', 'rolled', 'originally', 'newton', 'problem')
sent	('value', 'function')
confuse	('et', 'exhibited', 'notion')
wasn't	('range', 'confusing')
established	('usual', 'mathematical', 'been', 'whittaker', 'kolmogorov', 'convergence')
available	('function', 'undocumented')
undocumented	('available', 'wolfram')
command	('language',)
topology	('meaning', 'general')
connected	('open', 'codomain', 'set', 'intimately', 'one', 'intimately', 'though', 'run', 'component', 'quantities', 'formal')
open	('connected', 'denotes')
commutative	('under',)
element	('no', 'range', 'assumes', 'denoted', 'countably', 'quantity', 'standard', 'taken', 'taken', 'ordered', 'range', 'independently', 'quantum', 'become', 'covariance', 'list', 'list', 'pair', 'number', 'falling', 'bar', 'data', 'set', 'borel', 'fisher-tippett', 'same')
divisors	('no', 'domain')
codomain	('probability', 'connected')
map	('domain', 'natural', 'undefined', 'airy', 'range', 'over')
reinhardt	('range', 'domain')
surjection	('range',)
space	('event', 'probability', 'sample', 'daley', 'form', 'mark', 'mark', 'mark', 'mark', 'time', 'mark', 'double', 'simple', 'mark', 'point', 'set', 'assumed', 'possibility', 'probability', 'sample', 'contain', 'either', 'sample', 'trial', 'specified', 'domain', 'measurable', 'measure', 'probability', 'radon', 'state', 'measurable', 'probability', 'probability', 'measurable', 'measure', 'state', 'collection', 'baudin', 'lcs', 'molchanov', 'sample', 'set', 'sample', 'largest', 'sample', 'event', 'event', 'possibility', 'possibility', 'evans', 'sample', 'toss', 'sample', 'probability', 'probability', 'random', 'state', 'interpreted', 'locations', 'well;', 'work', 'convergence', 'fiber', 'fibration', 'measurable', 'state', 'doob', 'set', 'probability', 'random', 'state', 'variate', 'state', 'index', 'probability', 'random', 'state', 'representation', 'fock', 'over', 'completion', 'noise', 'fock', 'bounded', 'system', 'system', 'other', 'law', 'continuous', 'probability', 'sample', 'sample', 'trial', 'experimental', 'sample', 'sample', 'sample', 'sample', 'sample', 'measurable', 'measurable', 'measure')
failure	('rate', 'function', 'before', 'before')
hazard	('probability', 'function', 'probability', 'function', 'function', 'rate', 'p', 'function', 'rate', 'probability', 'function', 'ratio', 'function', 'function')
happen	('event', 'probability', 'probability', 'event', 'first', 'likely', 'diaconis')
happened	('fermat',)
force	('mortality', 'rate')
mortality	('force', 'probability', 'ratio')
pennies	('number', 'one', 'either', 'process', 'lose', 'ratio', 'your', 'player', 'number', 'greatest', 'most', 'casinos', 'individual')
flip	('two', 'one')
winning	('transfer', 'probability', 'probability', 'odd', 'probability', 'th')
transfer	('winning', 'penny')
loser	('penny',)
winner	('repeat',)
repeat	('winner', 'process')
eventually	('lose',)
lose	('eventually', 'pennies', 'only')
rendered	('respectively', 'penniless')
penniless	('rendered', 'your')
your	('penniless', 'pennies', 'opponent')
going	('chance', 'bankrupt', 'chance')
bankrupt	('going', 'equal', 'even')
opponent	('your',)
starting	('player', 'out', 'player', 'out', 'number', 'number', 'point', 'seed', 'point', 'output', 'including', 'including', 'reaching', 'point', 'lattice', 'one', 'other')
greatest	('pennies', 'chance', 'find', 'discrepancy')
gamble	('greater',)
wins	('casinos', 'first', 'he')
casinos	('wins', 'pennies', 'principle', 'always')
patrons	('principle',)
come	('always', 'out', 'up', 'still', 'out', 'still', 'out', 'set')
playing	('practice',)
skewed	('odd', 'favor', 'distribution')
favor	('skewed', 'house')
house	('favor', 'outcome')
quicker	('gambler',)
survival	('function', 'function', 'function', 'function', 'function', 'function', 'emulsion', 'time', 'function', 'function', 'function', 'p', 'function', 'similarly', 'function', 'probability', 'function', 'normalized', 'function')
mills	('probability', 'ratio', 'ratio', 'p', 'ratio')
iff	('conditional', 'campbell', 'appropriately', 'denotes', 'taken', 'multiple')
independence	('event', 'complement', 'experiment', 'axiom', 'deviation', 'observed')
complement	('independence', 'theorem', 'denotes', 'mutually', 'further', 'set')
talk	('sense', 'point')
rewritten	('finite', 'denotes', 'kenney', 'simpler')
little-o	('denotes',)
daley	('notation', 'vere-jones', 'literature', 'vere-jones', 'space', 'vere-jones', 'processes', 'vere-jones', 'work', 'vere-jones')
vere-jones	('daley', 'other', 'daley', 'pp', 'daley', 'interval', 'daley', 'point', 'daley', 'stationary')
ieif	('borel',)
pawlas	('measure', 'intensity', 'function', 'intensity', 'stationary', 'other')
symbolically	('denotes', 'defining', 'spp', 'done', 'separately')
notion	('value', 'intensity', 'oft-discussed', 'intensity', 'pp', 'interval', 'extend', 'interval', 'confuse', 'marked', 'point', 'light', 'crude', 'rise', 'interval', 'stationarity')
intimately	('measure', 'connected', 'process', 'connected')
oft-discussed	('one', 'notion')
stationary	('interval', 'interval', 'point', 'idea', 'point', 'interval', 'point', 'process', 'point', 'most', 'subset', 'number', 'process', 'location', 'point', 'though', 'crudely', 'light', 'definition', 'point', 'process', 'whenever', 'process', 'whenever', 'order', 'pawlas', 'vere-jones', 'point', 'weakly', 'process')
pointed	('interval', 'out', 'noted', 'out')
fundamentally	('though', 'different')
idea	('different', 'stationary', 'expressing', 'number')
stationarity	('interval', 'other', 'though', 'different', 'authors', 'notion', 'exist')
difficult	('done', 'extend', 'very')
extend	('difficult', 'notion', 'box', 'farthest')
stationarity;	('interval', 'doing')
doing	('stationarity;', 'significant', 'difference', 'standard')
machinery	('additional',)
significantly-increased	('overall', 'structural')
structural	('significantly-increased', 'complexity')
complexity	('structural', 'higher-dimensional', 'die', 'underlying')
higher-dimensional	('complexity', 'euclidean', 'get', 'brownian')
euclidean	('higher-dimensional',)
irrelevant	('mark', 'denotes', 'mark', 'mark', 'inclusion', 'mark', 'marking')
marked	('analysis', 'point', 'point', 'analysis', 'point', 'point', 'jacobsen', 'point', 'notion', 'point', 'analysis', 'point', 'analysis', 'point', 'analysis', 'point', 'analysis', 'point', 'analysis', 'point', 'probability', 'point', 'analysis', 'point', 'process', 'point')
weighting	('subject', 'normalized', 'clearly', 'condition')
scheme	('linear', 'weights')
unity	('sum', 'set', 'arbitrary', 'walk', 'probability', 'less', 'probability')
state	('axioms', 'real', 'measure', 'space', 'variable', 'space', 'algebra', 'space', 'original', 'before', 'space', 'variate', 'space', 'space', 'variable', 'space', 'actual', 'affairs')
weight	('kolmogorov', 'denotes', 'vertical', 'small', 'order', 'older', 'disinfectants', 'blood')
mutually	('complement', 'exclusive', 'event', 'exclusive', 'probability', 'exclusive', 'event', 'countable', 'exclusive', 'exclusive', 'principle', 'exclusive', 'event', 'exclusive', 'word', 'exclusive', 'sequence', 'independent')
exclusive	('mutually', 'mutually', 'occurrence', 'mutually', 'countable', 'mutually', 'probability', 'mutually', 'mutually', 'mutually', 'mutually')
hypothetical	('likelihood',)
yield	('occurred', 'specific', 'box', 'expectation', 'two', 'formed', 'solution', 'sequence', 'generalized', 'unexpected', 'uniformly')
concept	('outcome', 'respectively', 'generalization', 'random', 'chance', 'introduced')
configuration	('sample', 'probability')
stocker	('harris',)
expanded	('function', 'notation', 'guarantees', 'sum')
subfields	('various',)
importance	('particular', 'relative')
double	('space', 'simplifying', 'single', 'single', 'distribution', 'exponential', 'equal', 'term', 'summation')
spp	(';', 'definition', 'sequence', 'almost', 'symbolically', 'sequence')
never	('event', 'event', 'jacobsen', 'point', 'path', 'visits', 'origin', 'land')
marking	('point', 'occurrence', 'irrelevant', 'assign')
jacobsen	('never', 'marked', 'respectively', 'simple')
spatial	('process', 'point', 'process', 'temporal', 'process', 'point', 'process', 'temporal', 'process', 'point', 'process', 'temporal', 'process', 'point', 'process', 'temporal', 'process', 'point', 'process', 'temporal', 'point', 'plane', 'point', 'process', 'temporal', 'processes', 'temporal', 'process', 'point', 'process', 'point', 'process', 'temporal')
prove	('value', 'digit')
stipulated	('density',)
continued	('simple', 'using')
representation	('fraction', 'cuyt', 'space', 'brownian')
cuyt	('representation', 'et')
multidimensional	('point', 'set', 'point', 'one', 'point', 'baudin', 'point', 'one', 'point', 'analysis', 'point')
measurable	('process', 'triple', 'domain', 'probability', 'space', 'domain', 'space', 'probability', 'space', 'racs', 'variable', 'function', 'space', 'space', 'function', 'space')
accumulation	('containing',)
cardinality	('denotes',)
mpp	('though',)
exhibited	('should', 'confuse')
baudin	('set', 'multidimensional', 'space', 'talking', 'random')
ways	('occur', 'second', 'two', 'multiplication', 'ignorant', 'event', 'right', 'different', 'selection', 'selection', 'selection')
precludes	('one',)
samuel	('pepys',)
wrote	('pepys', 'isaac')
isaac	('wrote', 'newton')
letter	('long', 'asking', 'capital', 'most', 'capital', 'most', 'value', 'value')
asking	('letter', 'him')
him	('asking', 'probabilities', 'required', 'publish')
wager	('roll', 'he')
planned	('he',)
asked	('pepys', 'alternative', 'choose')
sixes	('two', 'dice', 'three', 'dice', 'probability', 'roll')
believed	('originally', 'last', 'limit', 'exist', 'limit', 'exist')
opined	('correctly', 'first')
highest	('outcome',)
conclusion	('newton',)
logic	('fact', 'hypothesis')
stigler	('analysis', 'probability')
a143163	('most',)
approaching	('asymptotically', 'zeilberger')
zeilberger	('approaching', 'gave')
gave	('zeilberger', 'sum')
monotonicity	('expression', 'self-evident')
self-evident	('monotonicity',)
inspection	('newton',)
colon	('probability', 'fraction')
portion	('probability', 'walk', 'economies')
probabilistic	('process', 'obey', 'type', 'obey', 'multivariate', 'experiment', 'axiom', 'experiment', 'experiment', 'time', 'experiment')
scatterings	('random',)
oftentimes	('point',)
revealed	('occurrence', 'one-by-one')
one-by-one	('revealed', 'time')
evolves;	('time',)
realization	('occurrence', 'point', 'consist')
archetypal	('regarded',)
possibility	('space', 'space', 'space')
enunciated	('first', 'jakob')
jakob	('enunciated', 'bernoulli')
ignorant	('bernoulli', 'ways')
believe	('reason', 'one', 'exponential', 'because', 'been')
preferentially	('occur', 'compared')
keynes	('likely', 'equal', 'strenuously')
indifference	('formulating',)
formulating	('indifference', 'no')
predicating	('reason', 'our')
our	('predicating', 'subject')
knowledge	('relatively', 'assertions')
assertions	('knowledge',)
strenuously	('keynes', 'opposed')
devoted	('principle', 'entire')
entire	('devoted', 'chapter', 's', 'probability', 'comprise', 'value')
chapter	('entire', 'book')
book	('chapter', 'attempt')
refute	('attempt', 'principle')
poincare	('principle', 'principle')
branch	('probability', 'mathematics')
studies	('mathematics', 'possible')
outcomes'	('together', 'relative')
certainty	('expressed',)
competing	('several', 'interpretations')
interpretations	('competing', 'actual')
frequentists	('probabilities', 'view')
view	('frequentists', 'probability', 'authors', 'temporal', 'latter', 'point')
conventional	('outcome', 'data')
treat	('bayesian', 'probability')
subjectively	('probability', 'statistical')
capital	('variate', 'letter', 'variate', 'letter')
contain	('space', 'possible', 'type')
empty	('intersection',)
countable	('probability', 'additivity', 'exclusive', 'mutually')
additivity	('countable', 'probability')
axiom	('probability', 'distribution', 'probability', 'independence', 'kolmogorov', 'outcome', 'probabilistic')
countably	('element', 'infinite')
experiment	('probability', 'independence', 'set', 'probabilistic', 'quantile', 'trial', 'independent', 'papoulis', 'event', 'probabilistic', 'probability', 'agreed', 'event', 'trial', 'probabilistic', 'occurrence', 'probabilistic', 'trial', 'sample', 'observation', 'under', 'well-defined', 'papoulis', 'event', 'lexis', 'named')
pdf	('continuous', 'function')
constrained	('satisfies', 'normalization', 'outputs', 'low-discrepancy', 'sequence', 'low-discrepancy')
condition	('special', 'topological', 'stochastic', 'holder', 'independent', 'weighting', 'minimum', 'replicate', 'kronecker', 'distribution', 'lindeberg', 'lindeberg', 'lyapunov', 'levy', 'limit', 'lindeberg', 'sufficient', 'lindeberg-feller', 'lindeberg', 'zabell', 'lindeberg', 'assumed', 'lindeberg', 'guarantees', 'lindeberg', 'limit', 'levy', 'normal', 'levy', 'normal', 'lyapunov', 'lyapunov', 'limit', 'sufficient', 'strong')
delta	('function', 'respectively', 'variance', 'integration', 'independent', 'interval', 'interval', 'interval', 'interval')
cornish	('distribution', 'fisher', 'expansion', 'fisher', 'polynomial', 'fisher', 'series', 'fisher')
unfortunate	('use', 'term', 'frequently', 'tendency')
superset	('probability',)
radon	('space', 'measure', 'measure')
mistakes	('find', 'proofreader', 'many', 'many', 'missed', 'proofreader', 'fraction', 'number', 'missed', 'proofreading', 'probability')
proofreader	('mistakes', 'mistakes')
missed	('mistakes', '?', 'mistakes', 'approximately')
?	('missed', 'total')
proofreading	('approximately', 'mistakes')
printer	('probability',)
monotonic	('probability', 'increasing', 'function', 'chisquaredistribution', 'choose')
gaps	('mean', 'leaves', 'different')
defines	('one', 'quantile', 'doob', 'stochastic', 'uspensky', 'de')
racs	('measurable', 'originally', 'general', 'case', 'talking')
locally	('setting',)
lcs	('topological', 'ambient', 'space')
topological	('lcs', 'condition', 'generalization', 'non-metrizable')
modified	('definition', 'collection', 'chamber', 'version', 'feller', 'version', 'theory', 'game', "'paradox'", 'version', 'montroll', 'bessel', 'root', 'unfair', 'moment', 'bessel', 'parameter', 'bessel', 'function', 'bessel', 'bessel', 'value', 'bessel', 'function', 'bessel', 'function', 'bessel')
ambient	('subset', 'lcs')
molchanov	('space', 'despite')
talking	('racs', 'baudin')
russian	('roulette', 'killed', 'roulette')
roulette	('russian', 'russian', 'probability')
chambers	('six', 'revolver', 'six', 'revolvers', 'revolvers', 'six', 'again')
revolver	('chambers', 'filled', 'case', 'six', 'less', 'because', 'variant', 'loaded', 'case', 'six', 'probability')
filled	('revolver',)
cartridges	('chamber',)
chamber	('cartridges', 'rotated', 'bet', 'rotates', 'modified', 'spin', 'fire')
rotated	('chamber',)
gun	('random',)
fired	('shooter',)
rotates	('chamber', 'place')
loaded	('he', 'revolver', 'single')
life	('case',)
revolvers	('chambers', 'chambers')
dying	('chance', 'ignoring')
ignoring	('dying', 'fact', 'again', 'imbalance', 'consecutive')
firing	('probability', 'round', 'bottom', 'pin')
round	('firing', 'always', 'mass', 'cylinder')
mass	('because', 'round', 'temperature')
imbalance	('cylinder', 'ignoring', 'real')
tend	('cylinder', 'stop', 'normal', 'normal')
rotating	('stop', 'heavy')
heavy	('rotating', 'side', 'iterations', 'solid', 'skewness')
pin	('firing', 'opposite')
blom	('version', 'et', 'et')
variant	('revolver', 'above', 'board')
cartridge	('two',)
duelists	('two', 'alternately')
alternately	('duelists', 'spin')
spin	('alternately', 'chamber', 'integer', 'particles', 'half-integer', 'particles')
fire	('chamber', 'themselves')
killed	('case', 'duelist', 'russian')
duelist	('first', 'killed')
nicolaus	('proposed',)
pays	('player', 'fixed')
dollars	('receives', 'coin', 'finite')
gain	('value', 'net', 'player')
money	('amount', 'wagered', 'amount', 'still')
wagered	('money', 'player')
nothing	('receives', 'trial')
concluded	('game', 'fair')
entrance	('fair',)
fee	('feller',)
modern	('feller', 'student', 'part', 'functioning')
hardly	('student', 'understand')
understand	('hardly', 'mysterious')
mysterious	('understand', 'discussions')
discussions	('mysterious',)
'paradox'	('modified',)
$2	('bet', 'no')
turn	('head', 'up', 'head', 'up', 'did', 'up', 'head', 'up', 'probability')
throw	('$4', 'second', 'did', 'expected')
$4	('throw',)
did	('throw', 'turn')
$8	('first',)
payoff	('player', 'final', 'net', 'misleading', 'without', 'large', 'long')
apparently	('player', 'hole', 'beyer')
hole	('apparently', 'amount')
clearly	('paradox', 'resolved', 'weighting')
resolved	('clearly', 'making')
net	('payoff', 'amount', 'mean', 'gain', 'number', 'quasirandom', 'word', 'several', 'sequence', 'polyhedron', 'planar', 'buekenhout', 'presentations', 'livio', 'p', 'polyhedron', 'polyhedra', 'might', 'labeled', 'shown', 'cube', 'regular', 'resembles', 'actually', 'polyhedron', 'uniquely', 'shephard', 'fukuda', 'set', 'term', 'term', 'technical', 'general', 'study', 'formally', 'set', 'set', 'random', 'set', 'graph', 'requirement', 'effect', 'method', 'quasi', 'requirement', 'effect')
won	('amount',)
account	('without', 'amount', 'lowered', 'number', 'lowered', 'number')
lost	('amount', 'previous', 'he')
previous	('lost', 'point', 'based', 'point', 'random', 'taken', 'ignore')
whopping	('player',)
balanced	('tail', 'large', 'group', 'anova')
win	('tosses', 'geometric', 'tosses', 'saint')
informally	('sample',)
sigma-algebra	('sample', 'sample')
tt	('sample',)
self-correcting	('process', 'denotes', 'process', 'occurrence')
intuitively	('process', 'process', 'point')
inhibits	('point', 'occurrence')
sure	('almost', 'absolutely', 'see')
interpreted	('space', 'either', 'form', 'stochastic', 'quantities', 'dot', 'power')
recording	('th',)
indication	('place', 'fewer', 'finite')
altogether	('occurred', 'respectively')
amalgamation	('paradox',)
reversal	('paradox',)
yule-simpson	('paradox',)
effect	('paradox', 'net', 'net', 'generating', 'disproportionate', 'real', 'amount', 'real', 'combined', 'observed', 'statistically', 'alternative', 'yule', 'time', 'approximately')
trend	('statistical', 'still', 'best-known')
segmented	('data', 'separate')
disappears	('data', 'ignored', 'properly', 'line', 'distribution')
whole	('simpson',)
simpson	('whole', 'paradox', 'accounted', 'paradox')
arise	('paradox', 'causal', 'number', 'heads-minus-tails', 'example', 'solving', 'number', 'one-dimensional')
accounted	('properly', 'simpson', 'proportion', 'proportion')
acquaintance	('one',)
network	('world',)
localized	('data', 'discrete', 'data', 'discrete')
locations	('set', 'set', 'space')
spatial-temporal	('point', 'particular', 'point', 'event', 'point')
location	('time', 'real', 'length', 'stationary', 'distribution', 'parameter', 'distribution', 'parameter', 'parameter', 'parameter')
spatiotemporal	('processes', 'point')
spatio-temporal	('processes', 'point')
space-time	('processes', 'point')
utilized	('most',)
lying	('point',)
crudely	('authors', 'stationary')
light	('stationary', 'notion')
crude	('notion',)
rise	('distinction', 'notion', 'process', 'binomial')
conclude	('function', 'point')
well;	('space', 'information')
bond	('analysis', 'percolation')
percolation	('bond', 'bootstrap', 'bootstrap', 'cayley', 'animal', 'theory', 'theory', 'threshold', 'site', 'martingale', 'theory', 'component', 'theory', 'site', 'truchet', 'density', 'run', 'theory')
cayley	('percolation', 'tree')
tree	('cayley', 'cluster', 'cluster', 'spanning', 'spanning', 'vertices-edges')
lattice	('perimeter', 'animal', 'walk', 'random', 'random', 'grid', 'path', 'same', 'point', 'walk', 'path', 'hypercubic', 'starting', 'same', 'point', 'breaking', 'step', 'triangular', 'conjectured', 'triangular', 'fall', 'distribution', 'distribution', 'integer', 'distribution')
animal	('lattice', 'percolation')
polyomino	('threshold', 'random')
site	('walk', 'percolation', 'simple', 'per', 'mean', 'theory', 'percolation', 'per', 'mean')
role	('important', 'many')
aspects	('many', 'economics')
science	('allowing', 'area', 'medicine', 'number', 'none')
allowing	('science', 'educated', 'distribution')
guesses	('educated', 'minimum')
expensive	('minimum', 'difficult-to-obtain', 'discrepancy')
difficult-to-obtain	('expensive',)
extant	('approximately', 'statistical')
maintained	('joke',)
chernoff	('problem', 'face', 'language', 'face')
moving	('likelihood', 'average', 'exponential', 'weighted', 'average', 'ewma', 'filter', 'exponential', 'average', 'analysis', 'average', 'blue', 'point', 'data', 'average', 'exponential', 'average', 'mean', 'median', 'point', 'average', 'analysis', 'average', 'analysis', 'average', 'smoothing', 'average', 'point', 'average', 'analysis', 'average', 'spencer', 'average', 'analysis', 'average', 'likelihood', 'average')
residual	('probability', 'square', 'treated', 'summed', 'minimized', 'coefficient', 'spline', 'best-fit', 'polynomial', 'partial', 'final', 'sum', 'form', 'should', 'coefficient', 'regression', 'regression', 'set', 'set', 'heteroscedastic', 'walk', 'variance')
vs	('predictor', 'case', 'predictor', 'predictor')
predictor	('vs', 'plot', 'vs', 'plot', 'vs', 'plot')
sharing	('run', 'problem')
consist	('realization', 'entries', 'random')
isolated	('time', 'probability', 'group', 'probability', 'group')
schoenberg	('integer', 'other')
two-element	('value', 'set')
liam	('point', 'prior')
perspective	('prior', 'viewing')
viewing	('perspective', 'temporal', 'latter', 'temporal', 'allow', 'nails', 'distribution', 'distribution')
parameters;	('time', 'latter')
modeled	('typically', 'specifying')
specifying	('modeled', 'conditional', 'merely', 'conditional')
indeed	('number', 'brownian', 's', 'sum', 'estimator', 'unbiased', 'motion', 'poisson')
merely	('processes', 'specifying')
lottery	('three', 'transylvania', 'probability', 'pick-', 'reservoir')
transylvania	('integer', 'lottery')
fano	('probability', 'plane')
shuffling	('algorithm', 'list', 'interleaving', 'shuffle', 'successively', 'normal', 'leaves')
generators	('bays',)
bays	('generators', 'shuffle', 'number', 'shuffle', 'number', 'shuffle')
shuffle	('bays', 'random', 'deck', 'exchange', 'random', 'riffle', 'riffle', 'bays', 'box', 'generally', 'rearrangement', 'shuffling', 'normal', 'randomize', 'card', 'random', 'bays', 'cards', 'exchange', 'monge', 'monge', 'out', 'out', 'riffle', 'riffle')
complex	('normal', 'disk', 'eigenvalue', 'spectrum', 'random', 'pair', 'number', 'set', 'disk', 'number', 'matrix', 'distribution', 'plotted', 'above', 'plane', 'product', 'position', 'object', 'square')
verified	('variance', 'solving', 'neither', 'shown')
generator	('number', 'iterating', 'simple', 'passes', 'number', 'random', 'random', 'produce', 'number', 'large', 'require', 'number', 'quasirandom', 'random', 'number')
seed	('simple', 'number', 'linear', 'number', 'goodness', 'computation', 'initial', 'system', 'starting', 'orbit', 'random')
passes	('generator', 'noise')
noise	('passes', 'random', 'sphere', 'examining', 'integration', 'space', 'white', 'power')
sphere	('test', 'noise', 'random', 'number', 'point', 'generating', 'distribution', 'point', 'differential')
randomness	('test', 'showing', 'stochastic')
showing	('randomness', 'no', 'graph', 'cumulative')
cliff	('structure', 'random', 'transformation', 'random')
discrepancy	('measure', 'computation', 'point', 'expensive', 'random', 'number', 'theorem', 'discrete', 'local', 'local', 'star', 'star', 'uniform', 'star', 'local', 'class', 'discrete', 'random', 'number', 'local', 'local', 'star', 'star', 'local', 'local', 'local', 'random', 'star', 'star', 'local', 'class', 'star', 'random', 'number', 'discrete', 'discrete', 'local', 'local', 'greatest', 'observed')
computationally	('set', 'matrices', 'unwieldy')
star	('discrepancy', 'discrepancy', 'cube', 'discrepancy', 'discrepancy', 'discrepancy', 'number', 'discrepancy', 'cube', 'discrepancy', 'origin', 'discrepancy')
cube	('star', 'local', 'net', 'buekenhout', 'star')
subintervals	('discrete', 'form', 'example', 'class', 'form', 'fact', 'vertex')
deck	('shuffle', 'cards', 'randomization', 'halves', 'riffle', 'color', 'normal')
successively	('cards', 'exchanging', 'shuffling', 'interchanging')
exchanging	('successively', 'cards')
goldstine	('odd', 'moews')
moews	('goldstine', 'goldstein', 'exchange')
shuffled	('most',)
goldstein	('likely', 'moews')
exchange	('moews', 'shuffle', 'position', 'cards', 'shuffle')
riffle	('number', 'shuffle', 'shuffle', 'deck', 'shuffle', 'shuffle')
eigenvalues	('set',)
concentration	('distribution', 'along', 'structure', 'line', 'mean')
accompanied	('line', 'slight')
paucity	('slight', 'above')
embedded	('below',)
girko	('uniform', 'circular', 'a046161', 'circular', 'matrix', 'circular', 'eigenvalue', 'circular')
eigenvalue	('number', 'random', 'hypergeometric', 'complex', 'spectrum', 'zonal', 'real', 'edelman', 'possibly', 'semicircle', 'lie', 'wigner', 'number', 'girko', 'correlation')
wigner	('matrix', 'semicircle', 'plane', 'semicircle', 'matrix', 'semicircle', 'real', 'law', 'observed', 'certain', 'eigenvalue', 'semicircle')
semicircle	('wigner', 'law', 'wigner', 'eigenvalue', 'wigner', 'law', 'obey', 'law', 'wigner', 'law')
hammersley	('two-dimensional', 'point', 'example', 'point', 'truncation', 'point', 'point', 'point', 'fibration', 'point', 'number', 'point', 'set', 'point')
calling	('fraction', 'p', 'set')
reversing	('number', 'binary', 'order')
truncating	('generalized',)
dimension	('representing', 'polytopes', 'results', 'matrix', 'number', 'like', 'greatly', 'walk', 'one', 'unit', 'above', 'yet')
truncation	('hammersley',)
quasirandom	('net', 'sequence', 'number', 'sequence', 'number', 'integration', 'number', 'integration', 'sequence', 'number', 'case', 'using', 'sequence', 'point', 'sequence', 'number', 'number', 'generator', 'sequence', 'method', 'sequence', 'aka', 'like', 'number', 'sequence')
kac	('normally', 'edelman', 'derived', 'derived', 'formula')
edelman	('kac', 'kostlan', 'kostlan', 'kostlan', 'function', 'et', 'et', 'kostlan', 'matrix', 'smallest', 'akemann', 'density', 'eigenvalue', 'first')
kostlan	('edelman', 'form', 'equation', 'edelman', 'edelman', 'edelman', 'asymptotic')
integrand	('above', 'expansion', 'oeis')
a093601	(';',)
modulus	('initial',)
congruence	('linear', 'method', 'linear')
pseudorandom	('number', 'number', 'decay', 'number', 'number', 'number', 'set', 'number', 'number', 'generating', 'distributed', 'reason', 'number')
inflection	('function', 'point', 'a133838')
applying	('point', 'logit', 'function', 'least', 'form', 'iteratively', 'procedure')
wagering	('type', 'bet')
doubled	('bet', 'halved', 'presented')
halved	('doubled', 'loss')
levy	('developed', 'described', 'distribution', 'flight', 'walk', 'distribution', 'walk', 'walk', 'flight', 'wiener', 'process', 'distribution', 'distribution', 'variable', 'nonnegative', 'distribution', 'distribution', 'distribution', 'sigma', 'distribution', 'distribution', 'flight', 'feller', 'condition', 'feller', 'condition', 'feller', 'condition')
developed	('levy', 'extensively', 'he', 'exact', 'number', 'wiener', 'moivre', 'normal')
extensively	('developed',)
one-dimensional	('doob', 'random', 'sequence', 'brownian', 'arise', 'random', 'interval', 'unit')
polyhedron	('diagram', 'net', 'above', 'net', 'general', 'figure', 'net', 'flattened', 'concave', 'graph', 'shephard')
satisfying	('set', 'certain', 'distribution', 'certain', 'number', 'probability', 'process', 'following')
uniformity	('certain', 'distribution')
planar	('pattern', 'net', 'polyhedra', 'hexagonal')
buekenhout	('net', 'parker', 'cube', 'parker', 'above', 'parker', 'solids', 'parker', 'graph', 'parker')
parker	('buekenhout', 'illustrations', 'buekenhout', 'buekenhout', 'number', 'buekenhout', 'platonic', 'buekenhout', 'conjectured')
illustrations	('parker', 'above')
tetrahedron	('classic', 'plane', 'similarly', 'geometric', 'median', 'median')
classic	('tetrahedron', 'treatise')
treatise	('classic', 'measurement')
compass	('measurement',)
ruler	('dürer',)
dürer	('ruler', 'one')
presentations	('first', 'net')
livio	('net',)
joined	('edge', 'might', 'point', 'line')
ambiguity	('might', 'several', 'avoid', 'papoulis')
polyhedra	('possible', 'net', 'folding', 'concave', 'constituent', 'convex', 'planar')
fold	('might', 'simple')
symmetrical	('simple',)
folding	('polyhedra', 'procedure')
labeled	('net', 'parameter', 'one', 'parameter')
solids	('different', 'constructed', 'platonic', 'summarized', 'base', 'buekenhout')
constructed	('solids', 'same', 'number', 'beginning')
tritetrahedron	('left',)
octahedron	('right',)
polytopes	('convex', 'dimension')
platonic	('results', 'solids', 'parker')
platonics	('duals',)
duals	('platonics', 'same')
unfoldings	('number', 'base')
base	('unfoldings', 'solids', 'sequence', 'van')
solid	('number', 'differential', 'thin', 'curve', 'heavy', 'curve')
resembles	('diagram', 'net')
basket	('above', 'handle')
spanning	('determined', 'tree', 'form', 'tree')
cut	('edge', 'form')
vertices-edges	('tree', 'graph')
amazingly	('conjectured', 'convex', 'been', 'distribution', 'distribution')
shephard	('net', 'statement', 'polyhedron', 'conjecture')
malkevitch	('statement',)
concave	('conjecture', 'polyhedra', 'one', 'example', 'polyhedron')
constituent	('polyhedra',)
overlap	('polygon', 'one')
flattened	('polyhedron', 'excess')
dodecahedron	('stella',)
stella	('dodecahedron',)
fukuda	('net', 'written')
routines	('written', 'unfold')
unfold	('routines', 'convex')
half-open	('point', 'interval')
volume	('interval', 'spherical', 'divide', 'uniformly', 'galaxies', 'average')
technical	('net', 'meaning')
moore-smith	('context',)
imbue	('analysis', 'non-metrizable')
non-metrizable	('imbue', 'topological')
convergence	('space', 'point', 'function', 'poor', 'function', 'greatly', 'etc', 'properties', 'established', 'sequence')
artifice	('properties', 'only')
alone	('sequence', 'provide', 'united', 'world')
adequate	('provide', 'dealing')
dealing	('adequate',)
continuity	('first-countable', 'distribution', 'correction')
first-countable	('continuity',)
riemann	('study', 'proposition', 'hypothesis', 'parameter', 'zeta')
mapping	('set', 'directed', 'random')
directed	('mapping', 'number', 'set')
fiber	('set', 'bundle', 'bundle', 'space')
bundle	('fiber', 'fiber')
fibration	('space', 'hammersley')
unfolding	('conjecture', 'uniform')
spherical	('point', 'factor', 'volume', 'real', 'coefficient', 'harmonic')
detect	('order', 'unexpected')
unexpected	('detect', 'structure', 'yield', 'connection')
bunching	('expected',)
ball	('number', 'point', 'dropping', 'down', 'smaller', 'perfectly', 'hit', 'dropped', 'time', 'bounce', 'falling', 'bernoulli', 'step', 'crosses', 'lower', 'sufficiently', 'height', 'heaps', 'characterized', 'over', 'drawn', 'probability', 'following')
picking	('point', 'random', 'point', 'example', 'uniform', 'order', 'improved', 'initial', 'repeated', 'urn', 'kotz', 'probability', 'problem')
archaic	('slightly', 'term')
computer-generated	('term', 'random', 'number', 'random')
prefix	('number', 'pseudo-')
pseudo-	('prefix', 'distinguish')
radioactive	('process',)
decay	('pseudorandom',)
computational	('useful', 'useful')
quasi-monte	('problem', 'carlo', 'carlo', 'carlo')
integration	('quasirandom', 'carlo', 'quasirandom', 'high', 'motion', 'ito', 'stochastic', 'noise', 'direct', 'similarly', 'proceed', 'delta', 'direct', 'probability')
quasi	('number', 'monte', 'net', 'monte')
fills	('sequence', 'uniformly')
low-discrepancy	('point', 'constrained', 'requirement', 'constrained')
ordinary	('sequence', 'uniform', 'example', 'van', 'term', 'lebesgue')
produce	('sequence', 'uniformly', 'generator', 'outputs', 'impossible', 'arbitrarily', 'human', 'string', 'always', 'same', 'should', 'positive')
big	('sequence', 'difference')
outputs	('produce', 'trial', 'sequence', 'constrained')
st	('interval', 'point')
halves	('two', 'probability', 'two', 'deck')
requirement	('low-discrepancy', 'net', 'net')
highly	('generated', 'correlated', 'point', 'correlated')
fine	('advance', 'grid')
stopping	('sequence', 'point', 'computation')
approach	('usual', 'halving', 'simplest', 'generate', 'procedure', 'violate', 'tail', 'zero', 'conservative', 'bonferroni', 'elegant')
halving	('approach', 'interval')
subsequent	('interval', 'table', 'cumulant', 'distribution', 'cumulant')
huge	('computation', 'number')
van	('theory', 'der', 'der', 'sequence', 'der', 'ordinary', 'der', 'base', 'der')
der	('van', 'corput', 'van', 'corput', 'van', 'corput', 'van', 'corput', 'van', 'corput')
corput	('der', 'sequence', 'der', 'der', 'der', 'sequence', 'der', 'sequence')
catherine	('one', 'proof')
prime	('important', 'number', 'beta', 'distribution', 'beta', 'beta', 'distribution', 'beta', 'beta', 'beta')
film	('theory',)
spectrum	('complex', 'eigenvalue', 'gaussian', 'power')
kanzieper	('derived', 'akemann', 'partition', 'akemann', 'erfc', 'akemann')
akemann	('kanzieper', 'summation', 'kanzieper', 'kanzieper', 'edelman')
summation	('akemann', 'direct', 'double', 'over', 'covariance', 'combining')
partitions	('length',)
complex-conjugated	('pair',)
zonal	('eigenvalue',)
partition	('kanzieper',)
parity	('matrix',)
vary	('entries', 'floor', 'properties', 'greatly', 'allowed')
laguerre	('generalized', 'generalized')
complementary	('polynomial', 'erf', 'erfc', 'nonnested', 'hypotheses', 'nonnested', 'hypotheses')
erfc	('kanzieper', 'complementary', 'interval', 'fisher')
integrating	('function', 'over', 'wallace')
half-plane	('multiplying',)
a046161	('girko', ';')
considers	('law', 'pp', 'expected')
a078416	('denotes',)
spectral	('matrix', 'function', 'density')
norm	('bougerol',)
bougerol	('norm', 'lacroix')
lacroix	('bougerol',)
viswanath	('pp', 'same')
code	('language', 'estimate', 'simple', 'drawing')
n;	('m', 'n', 'random')
selection	('distribution', 'large', 'random', 'random', 'based', 'sampling', 'implementation', 'ways', 'ways', 'ways', 'out', 'equal', 'successful', 'probability', 'hypergeometric', 'th', 'equal', 'expectation')
reproduces	('number', 'underlying', 'equation', 'linear')
required	('number', 'sum', 'breweries', 'him')
successive	('correlation', 'sequence', 'time')
reserved	('term', 'output')
output	('reserved', 'unpredictable', 'same', 'starting')
unpredictable	('output', 'physical')
course	('distribution',)
box-muller	('example', 'use')
impossible	('distribution', 'produce')
arbitrarily	('produce', 'long')
strangely	('very',)
predict	('actually',)
simplest	('number', 'linear', 'case', 'approach', 'technique', 'most', 'performed', 'most', 'most', 'distribution', 'discrete')
elegant	('simple', 'method', 'function', 'approach')
elementary	('method', 'cellular', 'use', 'row', 'matrix', 'column', 'slightly')
cellular	('elementary',)
automaton	('rule',)
require	('generator', 'specification', 'block', 'next')
specification	('require', 'initial')
goodness	('seed', 'random')
analyzed	('algorithm', 'examining')
differential	('distribution', 'area', 'stochastic', 'handled', 'definition', 'stochastic', 'equation', 'stochastic', 'equation', 'sphere', 'solid', 'identity', 'transformation', 'equation', 'generalizing', 'equation')
power-law	('generate', 'distribution')
schrage	('variable', 'algorithm')
abbreviation	('zero', 'random')
nonuniformly	('variate',)
simulation	('input', 'monte')
neelamkavil	('model',)
dynamical	('algorithm',)
orbit	('seed',)
randomization	('deck',)
rearrangement	('shuffle',)
interleaving	('shuffling', 'two')
interchanging	('successively', 'cards')
leaves	('shuffling', 'gaps')
layers	('two', 'cards')
randomizes	('cards', 'order')
keller	('cards', 'roughly')
randomize	('shuffle', 'bottom')
card	('shuffle', 'same', 'same', 'bloom', 'coin')
monge	('shuffle', 'shuffle')
vertex	('subintervals', 'joining')
etc	('observed', 'almost', 'almost', 'convergence', 'follow')
anderson	('number', 'darling', 'distribution', 'darling', 'test', 'darling', 'test', 'darling')
darling	('anderson', 'statistic', 'anderson', 'statistic', 'statistical', 'anderson', 'statistic', 'anderson', 'statistic')
kuiper	('statistic', 'statistic', 'test', 'statistic', 'statistic', 'statistic', 'tail', 'statistic', 'statistical')
synonymous	('stochastic', 'roughly')
greek	('word', 'origin')
parzen	('mean',)
counterpart	('stochastic', 'word')
phenomena	('random',)
involved	('stochastic', 'subtleties', 'using')
deterministic	('trial', 'number', 'random', 'random', 'analysis', 'time')
geometry	('stochastic', 'stochastic')
optimization	('stochastic', 'stochastic')
resonance	('stochastic', 'describing')
family	('process', 'random', 'process')
modeling	('important',)
seeks	('method', 'characterize')
construct	('characterize', 'well', 'derivative', 'matrix', 'block', 'stemleafplot', 'side-by-side')
halton	('number', 'point')
generality	('taken',)
maximally	('point', 'self-avoiding')
self-avoiding	('maximally', 'domain', 'walk', 'length', 'walk', 'similarly', 'walk', 'a046171', 'rook', 'a001997', 'walk', 'breaking', 'walk', 'two', 'two', 'maintain', 'number', 'over')
aka	('quasirandom',)
partitioning	('uniformly',)
drawbacks	('number', 'numerical')
like	('dimension', 'quasirandom')
arising	('matrices', 'quantum', 'distribution', 'benford')
quantum	('arising', 'mechanical', 'basic', 'stochastic', 'hudson-parthasarathy', 'stochastic', 'element', 'stochastic', 'classical', 'hudson-parthasarathy', 'stochastic', 'classical', 'mechanical', 'ampliation', 'stochastic', 'equation', 'mechanical', 'observables', 'flow', 'namely', 'stochastic')
mechanical	('quantum', 'quantum', 'evolution', 'quantum')
exception	('law', 'possesses')
possesses	('exception', 'curve')
transpositions	('randomly', 'performed', 'number', 'return')
return	('transpositions', 'berestycki', 'berestycki')
berestycki	('return', 'return', 'durrett', 'value', 'trott')
durrett	('berestycki', 'borel-tanner')
borel-tanner	('durrett', 'distribution', 'p', 'distribution')
trott	('distribution', 'plane', 'berestycki')
interestingly	('function', 'expected')
tanner	('borel', 'distribution')
real-valued	('stochastic',)
increments	('time', 'variable', 'normally', 'variance', 'nonoverlapping')
everywhere	('brownian',)
criteria	('above', 'brownian', 'variety', 'measure', 'purposes')
invariance	('natural', 'properties', 'scaling', 'scaling', 'under')
scaling	('including', 'invariance', 'invariance', 'mean')
moreover	('brownian', 'despite')
ill-behaved	('looking', 'first')
glance	('brownian',)
holder	('motion', 'continuous', 'walk', 'condition')
contrarily	('brownian',)
nowhere	('motion',)
wiener	('process', 'sausage', 'walk', 'process', 'walk', 'process', 'levy', 'walk', 'process', 'induced', 'process', 'measure', 'walk', 'process', 'example', 'process', 'process', 'walk', 'measure', 'sausage', 'term', 'line', 'sausage', 'analysis', 'developed', 'sequence')
sausage	('wiener', 'wiener', 'wiener', 'random')
kiyoshi	('lemma', 'ito')
noboru	('due', 'ito')
trajectories	('walk', 'composed')
self-similar	('composed',)
flight	('levy', 'random', 'levy', 'levy', 'normal')
pelya	('origin', 'watson', 'distribution', 'random', 'walk', 'random', 'one', 'random', 'walk', 'random', 'distribution')
watson	('pelya', 'mccrea', 'third', 'triple', 'walk', 'triple')
mccrea	('watson', 'whipple')
whipple	('mccrea', 'domb')
domb	('whipple', 'glasser')
glasser	('domb', 'zucker')
zucker	('glasser', 'oeis')
a086230	('oeis',)
a086231	(';',)
borwein	(';', 'bailey')
bailey	('borwein',)
ex	('third',)
modulo	('integral', 'multiplicative')
jacobi	('kind', 'theta')
theta	('jacobi', 'characteristic', 'th', 'properly')
montroll	('form', 'modified', 'value', 'flajolet')
flajolet	('montroll', 'finch')
a086236	('pólya',)
pólya	('a086236', 'random')
handled	('differential', 'use')
hudson	('formula', 'parthasarathy', 'follow', 'parthasarathy')
parthasarathy	('hudson', 'fock', 'hudson', 'stochastic')
fock	('parthasarathy', 'boson', 'space', 'reservoir', 'space')
boson	('processes', 'fock')
hilbert	('over', 'system')
completion	('space', 'linear')
span	('linear', 'exponential')
annihilation	('creation',)
creation	('annihilation', 'conservation')
conservation	('creation',)
fundamental	('two', 'domain', 'connects')
hudson-parthasarathy	('theorem', 'quantum', 'framework', 'quantum')
time-dependent	('general', 'adapted')
dependent	('time', 'adapted', 'several', 'distribution', 'time', 'outcome', 'two')
vacuum	('properties', 'characteristic')
framework	('within', 'hudson-parthasarathy')
evolution	('mechanical',)
unitary	('form', 'operator', 'operator')
tensor	('operator',)
reservoir	('fock', 'lottery')
self-adjoint	('notice',)
notice	('self-adjoint', 'equation')
identify	('what', 'variation', 'test')
ampliation	('operator', 'quantum')
analogue	('equation', 'heisenberg')
heisenberg	('analogue', 'equation', 'commutation')
observables	('quantum',)
flow	('quantum', 'bounded')
commutation	('operator', 'heisenberg')
canonical	('processes',)
restrictions	('set', 'allowed')
confined	('walk',)
physically	('random',)
thermal	('random', 'perturbations', 'molecules', 'equilibrium')
perturbations	('thermal', 'liquid')
liquid	('perturbations', 'responsible')
responsible	('liquid', 'random', 'walk')
collisions	('motion', 'molecules')
molecules	('collisions', 'gas', 'speeds', 'thermal')
gas	('molecules', 'random')
diffusion	('random',)
galton	('walk', 'board', 'problem', 'board', 'distribution', 'board', 'theorem', 'board', 'upright', 'mitrofanova', 'board')
avoiding	('self', 'walk', 'self', 'walk', 'self', 'walk', 'self', 'walk', 'self', 'polygon', 'self', 'walk', 'self', 'walk', 'self', 'walk')
connective	('walk', 'constant', 'walk', 'constant', 'lemma', 'constant', 'walk', 'constant')
examine	('quantities', 'probability', 'distribution', 'asymptotic', 'variable')
traveled	('distance', 'number')
toward	('step', 'one')
emphasized	('scatter', 'plot')
traveling	('probability', 'distance')
diagonally	('cell', 'below')
padded	('triangle', 'intervening')
intervening	('padded',)
evaluated	('sum', 'analytically', 'sum', 'analytically')
simplifying	('back', 'double', 'back')
a060818	(';',)
prevost	('stegun', 'hughes', 'stegun', 'hughes')
hughes	('prevost', 'prevost')
heads-minus-tails	('arise',)
graham	('ratio', 'et')
grünbaum	('shown', 'mosteller')
konig	('p', 'et', 'teth')
teth	('konig', 'proven')
most-visited	('three',)
catalan	('distribution', 'number')
phase	('notation', 'scrambled')
averaging	('variable', 'over')
travel	('order', 'distance')
reaching	('probability', 'point', 'probability', 'point', 'probability', 'starting')
infinity	('random', 'probability', 'binomial')
path	('walk', 'one', 'lattice', 'never', 'lattice', 'random', 'numbered', 'falling')
paths	('intersect', 'occur', 'number', 'number', 'number', 'oeis', 'number', 'point', 'length', 'oeis')
visits	('never', 'same')
horizontal	('positive', 'restricted', 'positive', 'restricted', 'only', 'vertical', 'median', 'line', 'lacked', 'hatched', 'strip', 'distribution')
a046171	('self-avoiding',)
rook	('self-avoiding',)
vertical	('horizontal', 'offsets', 'sum', 'difference', 'perpendicular', 'weight', 'least', 'regression', 'coordinate', 'actual', 'point', 'axis', 'rotation')
a007764	('number',)
abbott	('function', 'hanson')
hanson	('abbott', 'finch')
bending	('formed', 'piece')
piece	('bending', 'wire', 'stem')
wire	('piece', 'length', 'bends', 'cross')
bends	('plane', 'wire')
wires	('shape', 'length')
a001997	('self-avoiding',)
corner	('one', 'no')
a034165	(';',)
a034166	('self',)
staircase	('constant', 'polygon')
choice	('three', 'walk', 'presented', 'particular')
hypercubic	('walk', 'lattice')
ponitz	('general', 'tittman', 'computed', 'tittman')
tittman	('ponitz', 'tighter', 'ponitz', 'triangular')
tighter	('tittman', 'bounds')
bounds	('tighter', 'madras')
madras	('bounds', 'slade', 'conjectured', 'slade', 'exponent', 'slade', 'exponent', 'slade')
slade	('madras', 'conway', 'madras', 'following', 'madras', 'been', 'madras', 'been')
conway	('slade', 'guttmann')
guttmann	('conway', 'enumerated')
concatenating	('walk', 'two')
maintain	('necessarily', 'self-avoiding')
fekete	('us', 'lemma')
beyer	('constant', 'use', 'feller', 'distribution', 'freedom', 'authors', 'symbol', 'apparently')
noonan	('well', 'finch', 'improves', 'computed')
bound	('upper', 'improves', 'general')
improves	('bound', 'noonan')
alm	('plane', 'hexagonal')
exponent	('critical', 'madras', 'critical', 'madras', 'even')
induced	('function', 'wiener')
continuous-time	('stochastic',)
increment	('process', 'gaussian')
nonoverlapping	('increments', 'time', 'change')
norbert	('named',)
intended	('term',)
sausage-like	('essentially', 'tube')
tube	('sausage-like',)
cevian	('one',)
trapezoid	('line', 'median', 'triangle')
segment	('line', 'determined', 'continuous', 'slightly', 'tilted', 'line', 'range')
non-parallel	('two',)
kolmogorov-smirnov	('example', 'improve', 'distributed', 'improve')
smirnov	('kolmogorov', 'test', 'kolmogorov', 'test', 'kolmogorov', 'test', 'kolmogorov', 'test', 'kolmogorov', 'test')
decreasing	('statistical', 'maximum')
inversion	('weighted', 'statistic', 'function', 'count', 'weighted', 'weighted', 'statistic', 'statistic', 'statistic')
cramer	('count', 'major', 'faster', 'wallace', 'expansion', 'series', 'variance', 'converse', 'normal', 'distribution', 'theorem', 'distribution', 'distribution', 'theorem')
macmahon	(';', 'weighted')
degenhardt	('statistic',)
milne	('weighted',)
choose	('asked', 'best', 'monotonic', 'expand')
choice-specific	('conditional',)
linearly	('quantities', 'two-dimensional')
axes	('two', 'quantified')
quantified	('axes', 'correlation')
correlating	('coefficient',)
autocorrelation	('correlation', 'regression', 'correlation')
cross-correlation	('coefficient',)
pcc	('pearson',)
perason	('pearson', 'product-moment')
product-moment	('perason', 'correlation', 'coefficient', 'coefficient')
ppmcc	('bivariate',)
quality	('quantity', 'least', 'overall', 'fit', 'plot', 'control')
unnormalized	('quantities',)
increasingly	('fit', 'noisy')
noisy	('increasingly', 'data', 'number', 'data', 'fit', 'gaussian', 'angle', 'rotation')
interpretation	('see',)
best-fit	('solving', 'coincide', 'slope', 'generalized', 'line', 'coordinate', 'line', 'side', 'residual', 'line', 'form', 'producing', 'function', 'close', 'solving', 'euler', 'deviation', 'curve', 'using', 'parameter')
coincide	('best-fit', 'data')
equating	('◇',)
legendre	('uncorrelated', 'duplication', 'nonlinear')
duplication	('legendre',)
slope	('distributed', 'kenney', 'best-fit', 'line')
bevington	('see', 'use')
pugh	('pp', 'winslow')
winslow	('pugh',)
§12-8	('interested',)
interested	('§12-8', 'probability')
combining	('even', 'cosine', 'incorrectly', 'correct', 'moment', 'moment', 'order', 'total', 'summation')
cosine	('combining',)
skew	('solution', 'distribution')
surface	('variance', 'nail', 'kozlov')
guarantees	('definition', 'expanded', 'condition', 'individual')
eckhardt	('level', 'correlation')
best-fitting	('observed', 'curved', 'finding', 'curve')
curved	('best-fitting', 'line', 'because', 'flaring')
confluent	('ratio', 'hypergeometric', 'function', 'hypergeometric', 'moment', 'hypergeometric', 'regularized', 'hypergeometric', 'function', 'hypergeometric')
merit	('figure', 'function', 'regression', 'function', 'convention', 'function', 'value', 'function', 'value', 'function', 'p', 'function', 'regression', 'function')
gasser	('müller',)
müller	('gasser', 'technique')
offsets	('square', 'square', 'offset', 'square', 'outlying', 'vertical', 'line', 'perpendicular', 'least')
offset	('offsets', 'absolute', 'line', 'regression', 'elimination', 'applied')
treated	('residual', 'continuous', 'cannot')
outlying	('offsets', 'results', 'diminish')
disproportionate	('point', 'effect')
desirable	('property', 'problem')
minimized	('always', 'perpendicular', 'residual', 'find', 'always', 'perpendicular', 'function', 'distance', 'problem')
experimenter	('what', 'what', 'because')
wants	('uncertainties', 'uncertainties')
uncertainties	('wants', 'data', 'properties', 'most', 'wants', 'data')
incorporated	('along', 'along')
reasonable	('case', 'number')
quite	('fit', 'equal', 'likely')
graphed	('quantities', 'within')
additive	('within', 'multiplicative')
analyzing	('case', 'period')
period	('analyzing', 'pendulum', 'unit', 'quantity', 'quantity', 'value', 'unit', 'quantity', 'quantity', 'value', 'unit', 'quantity', 'quantity', 'value', 'unit', 'quantity', 'laspeyres', 'unit', 'quantity', 'quantity', 'value', 'unit', 'quantity', 'quantity', 'mitchell', 'unit', 'quantity', 'quantity', 'paasche', 'unit', 'quantity', 'quantity', 'walsh')
pendulum	('period', 'function')
iteratively	('applied', 'linearized', 'new', 'applying')
linearized	('iteratively', 'form', 'obtain', 'estimate')
achieved	('possible',)
linearize	('possible', 'nonlinear')
outset	('function', 'still')
resorting	('without', 'iterative')
implicit	('violate', 'assumption')
acceptable	('still', 'results', 'compare', 'significance', 'fraction')
pseudoinverse	('type', 'fitting', 'regression', 'matrix', 'matrix', 'moore-penrose', 'moore-penrose', 'matrix', 'matrix', 'matrix', 'most', 'encountered', 'moore-penrose', 'type', 'matrix', 'matrix', 'regression')
poor	('fit', 'convergence', 'sample', 'agreement')
differently	('weighted', 'order')
high-quality	('order',)
proceeds	('fitting', 'finding')
minimize	('procedure', 'actual', 'use', 'better', 'function', 'sum')
unsquared	('sum', 'using')
seem	('might', 'appropriate')
discontinuous	('results',)
summed	('residual',)
disproportionately	('point', 'large')
lead	('fit', 'polynomial', 'superscripts', 'outcome')
dot	('interpreted', 'plot', 'plot', 'two', 'same', 'unfilled', 'maximum', 'plot', 'plot', 'plot', 'draw', 'number', 'drawing', 'plot', 'ticks', 'plot', 'interval', 'plot')
parameterized	('fit',)
fitted	('point', 'point')
acton	('variance',)
gonick	('pp', 'smith', 'side', 'smith')
manova	('law', 'matrix', 'fitting', 'replicate', 'analysis', 'p', 'statistical', 'procedure', 'negative')
penrose	('moore', 'matrix', 'moore', 'matrix', 'moore', 'variously', 'moore', 'matrix', 'moore', 'matrix', 'moore', 'matrix', 'moore', 'matrix')
spline	('residual',)
better	('equally', 'minimize', 'probability', 'inequalities')
short-dashed	('plot', 'curve')
long-dashed	('◇', 'curve')
amenable	('minimizing', 'analytic')
former	('minimum', 'latter')
second-	('minimizing', 'higher-order')
generalizing	('straight', 'type', 'differential')
dropping	('again', 'number', 'ball')
superscripts	('lead',)
vandermonde	('form', 'fitting', 'matrix')
premultiplying	('writing', 'solved', 'seen')
transpose	('first', 'matrix', 'true')
moore-penrose	('matrix', 'matrix', 'matrix', 'generalized', 'pseudoinverse', 'pseudoinverse', 'inverse', 'pseudoinverse', 'matrix')
campbell	('iff', 'meyer')
meyer	('campbell', 'matrix')
operations	('row', 'through', 'same', 'identity', 'column', 'through', 'same', 'identity')
premultiplication	('through', 'nonsingular')
postmultiplication	('through', 'nonsingular')
block	('form', 'construct', 'mean', 'length', 'require', 'next', 'sequence', 'third', 'length', 'length', 'building', 'other')
appropriately	('iff', 'dimensional')
jodár	('matrices', 'et')
drazin	('regression', 'inverse', 'regression', 'inverse')
figure-of-merit	('function', 'function')
agreement	('measure', 'data', 'small', 'process', 'argue', 'test', 'poor', 'fact', 'only', 'correlation')
adjusted	('parameter', 'based')
approximated	('closely', 'chebyshev', 'characteristic', 'distribution', 'distribution', 'normal', 'function', 'distribution', 'normal')
variously	('penrose', 'generalized')
conjugate	('satisfies',)
overdetermined	('parameter', 'set', 'solve', 'set')
desire	('equation', 'solve')
pick	('equation', 'initial', 'probability')
reduce	('change', 'written', 'log', 'rayleigh')
concise	('matrix',)
elimination	('offset',)
new	('applied', 'iteratively', 'indexes', 'york', 'average', 'sequence', 'distributed', 'distribution', 'deviation', 'variable')
prescribed	('smaller',)
converge	('procedure', 'very', 'poisson')
improved	('greatly', 'picking')
iteration	('example',)
thin	('shown', 'solid')
dotted	('guess',)
intermediate	('curve', 'value', 'computed', 'case', 'v')
iterations	('heavy',)
converged	('guess',)
could	('technique', 'obviously', 'probability', 'occurred')
obviously	('could', 'generalized')
worsen	('generally', 'number')
increased	('analogous',)
euler	('best-fit', 'distribution', 'mascheroni')
rotation	('noisy', 'vertical')
proceed	('equation', 'integration', 'noting')
projection	('equation', 'matrix')
goodness-of-fit	('using', 'test')
criterion	('most', 'ordered', 'sufficient')
fractal	('regression', 'least')
anticorrelated	('perfectly', 'statistical')
self-describing	('sequence',)
preceding	('digit',)
append	('two', 'obtain')
fifth	('fourth',)
a006928	('sequence', 'except')
a042942	('sequence', 'recurrence')
started	('sequence', 'above')
undertaken	('procedure', 'beginning')
beginning	('undertaken', 'last', 'constructed', 'forming')
virtually	('last', 'identical')
a000002	('same',)
a001083	('essentially',)
kolakoski	('plot', 'sequence', 'a118270', 'constant', 'equidistributed', 'sequence')
a118270	('kolakoski',)
unsettled	('above',)
certainly	('digit', 'consistent')
equidistributed	('kolakoski', 'distribution', 'sequence')
clump	('probability', 'always', 'six')
urn	('picking', 'containing', 'drawn')
distinguishable	('two',)
replacement	('object', 'collection')
a050233	('special',)
a086253	('positive',)
a086254	('positive',)
unfair	('modified',)
success	('probability', 'probability', 'probability', 'constant', 'probability', 'trial', 'proportion', 'probability', 'probability', 'trial', 'negative', 'characteristic', 'trial', 'th')
continuing	('expected',)
longest	('run', 'expected')
gordon	('run', 'et')
schilling	('et', 'number')
arrangements	('possible',)
johnson	('coefficient', 'kotz', 'moment', 'et', 'stegun', 'et')
kotz	('johnson', 'picking')
indistinguishable	('containing', 'type')
bloom	('coefficient', 'following', 'jackson', 'card', 'expected')
goulden	('term', 'jackson', 'interval', 'confidence')
jackson	('goulden', 'bloom')
color	('same', 'deck')
a086440	('normalizing',)
normalizing	('a086440', 'multiplying')
a086438	('disproves',)
disproves	('a086438', 'assertion')
assertion	('disproves', 'gardner')
noncontiguous	('number', 'split')
split	('noncontiguous', 'sequence')
maximal	('sequence', 'clumps')
clumps	('maximal', 'same', 'number', 'length')
eulerian	('tossing', 'number')
run-length	('list', 'encoding', 'encoding', 'encoding')
encoding	('run-length', 'run-length', 'run-length', 'wolfram', 'length')
look	('run', 'say')
horizontally	('adjacent', 'vertically')
vertically	('horizontally', 'fall', 'onto')
a086266	('number',)
a086265	('total',)
a086268	(';',)
ziff	(';', 'et')
truchet	('percolation', 'tiling')
formal	('class', 'series', 'connected', 'series', 'function', 'identity', 'identical', 'expansion')
edgeworth	('parameter', 'series', 'charlier', 'expanding', 'expansion', 'series', 'series', 'series', 'function', 'series', 'valid', 'series', 'marshall', 'index', 'marshall', 'index')
gram-charlier	('series', 'derivative')
pairwise	('identity', 'identity', 'different')
collecting	('expanding', 'series')
a-series	('identical', 'polynomial')
hermite	('expansion', 'combination')
faster	('zero', 'cramer')
szego	('wallace', 'charlier')
moivre-laplace	('de', 'theorem')
successes	('number', 'probability', 'number', 'number', 'least', 'least', 'out', 'large', 'difference', 'continuous', 'number', 'suppose', 'observed', 'distribution', 'out', 'distribution', 'out', 'probability', 'observed', 'probability', 'probability', 'number', 'sample')
corollary	('probability',)
moivre	('de', 'laplace', 'de', 'developed', 'de', 'laplace')
weak	('distribution', 'law', 'large', 'law', 'number', 'law', 'law', 'pp', 'law')
developing	('take', 'function')
laspeyres'	('index', 'index', 'index')
paasche	('index', 'index', 'index', 'index', 'index', 'period', 'index')
indices	('statistical', 'index', 'statistical', 'index', 'statistical', 'index', 'statistical', 'index', 'type', 'among', 'statistical', 'bowley', 'statistical', 'index', 'statistical', 'index', 'statistical', 'index', 'statistical', 'index', 'statistical', 'index')
quantify	('order', 'proposed', 'fatigue')
best-known	('trend', 'index')
consumer	('united', 'price')
inflation	('value', 'based')
dow	('product', 'jones')
jones	('dow', 'nasdaq')
nasdaq	('jones', 'indexes')
indexes	('nasdaq', 'new')
york	('new', 'american')
american	('york', 'stock')
stock	('american',)
listed	('those', 'following')
marshall-edgeworth	('index',)
mitchell	('index', 'index', 'index', 'period', 'index')
walsh	('index', 'index', 'index', 'index', 'period', 'index')
laspeyres	('index', 'index', 'period', 'index')
marshall	('index', 'edgeworth', 'unit', 'edgeworth')
bar	('graph', 'element', 'charts', 'data', 'chart', 'plot', 'chart', 'plot', 'chart', 'combines', 'plot', 'chart', 'arc', 'chart')
categories	('one', 'indicated', 'percentage', 'data', 'pareto')
height	('rectangle', 'width', '@@@', 'heaps', 'ball')
charts	('bar', 'wolfram')
chart	('bar', 'statistical', 'pie', 'type', 'histogram', 'bar', 'box', 'bar', 'bihistogram', 'pie', 'sheppard', 'displaying', 'bar', 'plotting', 'pie', 'wolfram', 'pie', 'statistical', 'bar', 'circular')
pie	('plot', 'chart', 'ogive', 'chart', 'emphasis', 'chart', 'data', 'chart')
bland-altman	('plot', 'difference', 'instance')
simultaneously	('method', 'performed', 'alpha', 'uniseriate', 'solving', 'writing')
determination	('easier', 'two', 'test', 'problem', 'test')
cartesian	('point',)
mean-difference	('plot', 'tukey')
tendency	('plot', 'up', 'unfortunate', 'invoke')
medicine	('science', 'under', 'test', 'test')
names	('ma', 'summarizes', 'various')
ma	('names', 'ra')
ra	('ma',)
dna	('study',)
microarrays	('one',)
motivating	('one',)
behind	('factor', 'technique')
experts	('many', 'attempt')
argue	('incorrectly', 'agreement')
bland	('correlation', 'altman', 'test', 'altman', 'plot', 'altman', 'plot', 'altman', 'plot', 'altman')
altman	('bland', 'because', 'bland', 'plot', 'bland', 'plot', 'bland', 'plot', 'bland', 'plot')
affect	('scale', 'only')
fèvre	('correlation', 'transforming')
thereof	('difference', 'accurately')
accurately	('thereof', 'summarizes')
box-and-whisker	('plot', 'create', 'p')
displaying	('method', 'method', 'simple', 'chart')
invented	('data', 'diagram', 'john')
draw	('plot', 'box', 'quartile', 'statistical', 'box', 'value', 'side', 'side', 'bin', 'dot', 'bin', 'stack')
farthest	('extend',)
closely-related	('definition', 'lesser')
lesser	('closely-related',)
lacked	('formulation', 'horizontal')
crossbars	('extended', 'dashed', 'adjacent')
drew	('point', 'unfilled')
unfilled	('drew', 'dot')
hatched	('maximum', 'horizontal')
strip	('horizontal',)
figure;	('left', 'tukey')
identifying	('value',)
labels	('explicit', 'tukey')
dashed	('ending', 'ending', 'crossbars')
ending	('dashed', 'dashed')
eyebrow	('instance', 'size')
slant	('eye', 'nose')
eye	('slant', 'eccentricity', 'size', 'spacing')
nose	('size', 'slant')
characteristics--head	('using',)
eccentricity	('eye', 'pupil')
spacing	('eye',)
pupil	('eccentricity',)
mouth	('size', 'shape', 'size')
against	('frequency', 'upper', 'plotting', 'parameter', 'evidence', 'null', 'compare', 'critical')
stack	('draw',)
inclusively	('simple',)
labeling	('appropriate', 'bin')
@@@	('height',)
ticks	('m', 'dot')
stem	('histogram', 'leaf', 'correction', 'leaf', 'side-by-side', 'leaf', 'piece', 'leaf', 'plot', 'leaf')
leaf	('stem', 'diagram', 'stem', 'diagram', 'stem', 'stem', 'diagram', 'stem', 'diagram')
smooth	('curve', 'make', 'nearly')
limiting	('curve', 'case', 'pearson', 'distribution', 'distribution', 'case', 'variate', 'cumulative')
bihistogram	('chart', 'bin')
display	('value', 'statistical')
combines	('application', 'bar')
statisticalplots`	('pareto', 'quantile', 'quantile', 'above')
numeric	('plotting',)
wedges	('circular', 'arc', 'amount', 'taken')
arc	('wedges', 'plot', 'bar')
comprise	('together', 'entire')
center	('disk', 'emphasis')
emphasis	('center', 'pie')
sector	('circular', 'histogram')
q	('plot',)
q-q	('plot',)
stem-and-leaf	('diagram', 'tukey')
quickly	('diagram', 'summarizes')
maintaining	('data', 'individual')
removing	('data', 'last')
sorted	('column', 'numerical')
john	('invented',)
stemleafplot	('construct', 'statistical')
side-by-side	('construct', 'stem')
splitting	('plot', 'data')
contrary	('testing', 'null', 'hypothesis', 'null')
null	('contrary', 'testing', 'hypothesis', 'reject', 'hypotheses', 'hypothesis', 'hypothesis', 'formulate', 'truth', 'observed', 'against', 'significant', 'hypothesis', 'hypothesis', 'hypothesis', 'reject', 'hypothesis', 'contrary', 'hypothesis', 'hypothesis', 'testing', 'hypothesis', 'term', 'term', 'rejection', 'acceptance', 'term', 'test', 'hypothesis', 'term', 'test', 'hypothesis')
superposed	('alternative',)
improve	('statistic', 'kolmogorov-smirnov', 'statistic', 'kolmogorov-smirnov')
heterogeneity	('test',)
restricting	('anova', 'same', 'using', 'set', 'set')
f-ratio	('mean',)
ss	('mean',)
reject	('small', 'null', 'one', 'null')
replicate	('manova', 'variance', 'condition')
universe	('normal', 'unknown', 'normal', 'unknown', 'distributed', 'mean', 'mean', 'normal', 'form')
universes	('two', 'common')
multiple-comparison	('correction', 'correction', 'specificity')
avoid	('order', 'lot', 'order', 'lot', 'upon', 'ambiguity')
lot	('avoid', 'spurious', 'avoid', 'spurious')
lowered	('need', 'account', 'need', 'account')
conservative	('most', 'approach', 'bonferroni', 'less')
hypotheses	('test', 'under', 'assumption', 'statistical', 'null', 'nested', 'complementary', 'complementary')
false	('individual', 'test', 'test', 'error', 'negative', 'hypothesis', 'positive', 'error', 'positive', 'hypothesis', 'negative', 'sensitivity', 'negative', 'specificity', 'positive', 'accept', 'positive', 'rejection', 'hypothesis', 'negative', 'acceptance', 'test', 'hypothesis', 'accepted', 'positive', 'rejected', 'negative', 'probability', 'probability')
experiment-wide	('value', 'critical')
subtleties	('value', 'involved')
one-parameter	('fitting', 'solution')
calculating	('value', 'three')
parabola	('fit',)
cuzzi	('point',)
answer	('unique', 'because')
behrens	('fisher', 'problem', 'fisher', 'problem', 'fisher', 'problem')
nonrandom	('test',)
looked	('fisher', 'he')
chi-square	('pearson', 'difference')
likelihood-ratio-test	('other',)
mentioned	('measure', 'above')
remain	('above', 'applicable')
applicable	('remain', 'lippmann')
journal	('say', 'association', 'type')
articles	('number', 'topics', 'five', 'math')
topics	('articles', 'mathematics')
biology	('mathematics', 'appearing', 'relevant')
issue	('appearing', 'one')
journals	('mathematics',)
magazine	('five',)
article	('type',)
proposition	('hypothesis', 'consistent', 'postulate', 'riemann')
neither	('been', 'verified', 'function', 'range', 'distribution', 'continuous')
implication	('second',)
predicate	('general',)
bourget	('hypothesis', 'hypothesis')
chinese	('hypothesis', 'hypothesis')
continuum	('conjecture', 'hypothesis', 'hypothesis')
monster	('testing', 'barring')
barring	('monster', 'nested')
nested	('barring', 'hypothesis', 'test', 'hypotheses', 'testing', 'likelihood', 'model', 'hypothesis', 'hypothesis', 'subset', 'hypothesis')
postulate	('hypothesis', 'proposition')
schinzel	('hypothesis', 'hypothesis')
souslin	('hypothesis', 'hypothesis')
formulate	('step', 'null')
combined	('effect', 'component')
assess	('statistic', 'truth', 'case', 'hypothesis')
truth	('assess', 'null')
stronger	('smaller', 'evidence')
evidence	('stronger', 'against')
compare	('hypothesis', 'acceptable', 'd-statistic', 'against', 'data', 'likelihood')
i	('type', 'error', 'type', 'error', 'type', 'error', 'type', 'type', 'error', 'type', 'error', 'type', 'error', 'type', 'type', 'beta', 'case')
ii	('type', 'error', 'type', 'error', 'type', 'error', 'type', 'type', 'error', 'type', 'error', 'type', 'error')
d-statistic	('compare', 'sample', 'greater')
nonnested	('test', 'complementary', 'test', 'complementary')
sensitivity	('ratio', 'specificity', 'ratio', 'specificity', 'test', 'specificity', 'statistic', 'statistical', 'test', 'statistical', 'value', 'specificity', 'probability', 'false', 'true', 'value', 'significance', 'hypothesis', 'specificity', 'hypothesis', 'specificity')
specificity	('sensitivity', 'sensitivity', 'sensitivity', 'statistical', 'test', 'statistical', 'statistic', 'statistical', 'sensitivity', 'statistical', 'following', 'false', 'multiple-comparison', 'test', 'type', 'sensitivity', 'statistical', 'sensitivity', 'statistical')
observing	('likelihood', 'actual')
response	('multiple',)
uniseriate	('simultaneously', 'case')
consideration	('no',)
everitt	('situations', 'wykes')
wykes	('everitt',)
nlr	('negative',)
possibilities	('set', 'satisfy', 'set', 'satisfy', 'take')
neyman	('size', 'pearson')
tested	('hypothesis', 'possible')
rejection	('possible', 'under', 'false', 'null')
determines	('paired', 'differ')
predictive	('positive', 'value', 'negative', 'value', 'statistic', 'value', 'test', 'value', 'test', 'value')
*	('denoted',)
**	('authors',)
recommended	('significance',)
main	('two',)
affairs	('state', 'observed')
name	('true', 'logistic', 'derive', 'fact')
suppose	('example', 'you', 'size', 'successes', 'variate', 'quadratic')
measuring	('you', 'leg')
leg	('measuring', 'length')
eight	('length', 'different', 'repeated')
lizard	('different', 'species')
species	('lizard', 'wanted')
wanted	('species', 'see')
significantly	('differ',)
willing	('people', 'accept')
accept	('willing', 'false')
acceptance	('false', 'null')
accepted	('hypothesis', 'false')
rejected	('hypothesis', 'false')
z	('observation', 'score', 'fisher', 'distribution', 'using', 'student', 'distribution')
ema	('abbreviated',)
ewma	('moving',)
filter	('moving', 'applied', 'golay')
older	('weight',)
spencer	('median', 'point', 'average', 'formula', 'actuaries', 'point', 'average', 'formula', 'difference', 'moving', 'explicitly', 'formula')
nonstationary	('series', 'joint', 'index', 'time')
predictability	('time', 'linear', 'entropy', 'time', 'analysis')
redundancy	('linear', 'linear', 'matrix', 'time')
entropy	('predictability', 'joint', 'linear')
forecasting	('problem', 'future')
weakly	('value', 'stationary')
irregular	('generate', 'oscillation')
oscillation	('irregular', 'even')
slutzky	('data', 'yule')
yule	('slutzky', 'effect')
modification	('set',)
nearly	('smooth', 'continuous')
diminish	('remove', 'outlying')
smoothing	('point', 'time', 'graph', 'moving', 'average')
savitzky	('average', 'golay')
golay	('savitzky', 'filter')
actuaries	('spencer',)
daily	('series', 'temperature')
temperature	('daily', 'mass')
monthly	('measurement',)
sales	('yearly',)
yearly	('sales', 'population')
goals	('figure', 'time')
forecast	('data', 'future')
heartbeat	('usage', 'analysis')
castiglioni	('time',)
periodogram	('average', 'prediction')
forming	('beginning', 'outer')
stage	('sequence', 'concatenated')
concatenated	('stage', 'form')
waveform	('phenomenon', 'sampled')
shifted	('slightly',)
jitter	('average',)
ghost	('trial', 'sampling')
lexis	('set', 'supernormal', 'ratio', 'trial', 'variance', 'trial', 'ratio', 'trial', 'ratio', 'trial', 'set', 'trial', 'experiment')
supernormal	('lexis', 'subnormal', 'subgroup', 'trial')
subnormal	('trial', 'supernormal', 'trial', 'ratio', 'number', 'number', 'subgroup', 'trial')
longitudinal	('data', 'data')
experimental	('space',)
description	('determined', 'variable', 'relative')
agreed	('experiment', 'upon')
rolling	('coin',)
purposes	('criteria', 'investigating')
investigating	('purposes', 'properties')
re	('distribution', 'error', 'confidence')
se	('error', 'standard')
tries	('number', 'relative')
implementation	('selection', 'statistical')
vital	('sampling', 'part', 'use', 'functioning')
polling	('market',)
market	('polling',)
manufacturing	('proper',)
functioning	('vital', 'modern')
economies	('portion',)
processing	('signal', 'measurement')
intension	('time', 'reconstructing')
reconstructing	('intension', 'original')
infinite-precision	('signal', 'sampling')
band-limited	('sampling', 'signal')
nyquist	('signal', 'trial', 'sampling', 'oversampling')
signal-to-noise	('frequency', 'undersampling')
undersampling	('signal-to-noise',)
thompson	('decrease', 'et')
oversampling	('nyquist', 'quantization')
quantization	('oversampling', 'efficiency')
shah	('theorem', 'function')
sinc	('function', 'function')
subgroup	('subnormal', 'supernormal')
performance	('single', 'well-defined', 'bernoullidistribution', 'fixed')
well-defined	('performance', 'experiment')
apex	('down', 'triangular')
notational	('two',)
ranging	('value', 'domain')
binormal	('distribution',)
particles	('spin', 'spin', 'silver', 'photographic')
lerch	('integral', 'integral', 'term')
polylogarithm	('bose', 'fermi')
bose	('polylogarithm', 'einstein', 'distribution', 'einstein')
einstein	('bose', 'distribution', 'distribution', 'bose', 'distribution', 'distribution')
fermi	('function', 'dirac', 'distribution', 'dirac', 'polylogarithm', 'dirac')
dirac	('fermi', 'distribution', 'fermi', 'distribution', 'fermi', 'distribution')
sigmoid	('distribution', 'function', 'function', 'function', 'function', 'function')
lorentzian	('distribution', 'distribution', 'equation', 'function', 'distribution')
lorentz	('distribution', 'distribution')
tilted	('segment', 'random')
x	('represent',)
cauchy	('general', 'distribution', 'median', 'distribution', 'distribution', 'distribution', 'variate', 'distribution', 'distribution', 'parameter', 'distribution', 'distribution', 'distribution', 'case', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'distributed', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution', 'distribution')
undefined	('distribution', 'map')
diverge	('integral', 'uniform')
typo	('et',)
chisquaredistribution	('monotonic',)
via	('cumulant', 'characteristic', 'distribution', 'simpler')
mercator	('side',)
noncentral	('distribution', 'chi-squared', 'distribution', 'chi', 'distribution', 'f', 'chi-squared', 'moment', 'chi', 'doubly', 'distribution', 'distributed', 'chi-squared', 'singly', 'case', 'doubly', 'doubly', 'distribution', 'singly', 'gamma', 'singly', 'analytically', 'variance', 'f', 'student', 'student', 'variance', 'student', 'many', 'unimodal', 'formula', 'student')
snedecor	('distribution', 'statistical', 'distribution', 'student', 'student', 'function', 'distributed', 'p', 'f')
rice	('distribution', 'distribution', 'distribution', 'distribution')
joins	('function', 'univariate')
copula	('two-dimensional', 'function', 'function', 'continuous', 'function', 'distribution')
sklar	('distribution', 'theorem', 'unique', 'theorem')
relaxation	('deviation',)
waiting	('function', 'distribution', 'processes', 'function', 'function')
erlang	('distribution', 'variable', 'distribution', 'case', 'distribution', 'distribution', 'distribution', 'distribution')
lambda	('exponential', 'th', 'th')
memoryless	('random', 'random', 'variable', 'only', 'random', 'two', 'definition', 'integer', 'definition', 'two', 'consequence', 'property', 'value', 'general')
subfactorial	('first',)
heaviside	('function', 'step', 'function', 'step', 'term', 'step', 'function', 'step')
fisher-tippett	('type', 'extreme', 'element', 'distribution', 'type', 'extreme')
log-weibull	('maximum',)
apery	('constant', 'constant', 'moment')
frechet-type	('weibull-type',)
weibull-type	('frechet-type', 'beta', 'distribution')
gumbel-type	('distribution', 'distribution')
two-parameter	('distribution', 'weibull')
mascheroni	('euler',)
half-integer	('study', 'spin')
tippett	('fisher', 'distribution')
fischer	('general',)
jacobian	('sum', 'ratio')
pochhammer	('moment', 'moment')
gibrat	('distribution', 'excess', 'distribution', 'case')
expressible	('variance', 'closed')
multivariate-distributed	('gaussian', 'zero')
mahalanobis	('sample', 'distance')
dimensionality	('multivariatestatistics`', 'parameter')
had	('p', 'probability')
identically-distributed	('independent', 'independent')
direct	('excess', 'integration', 'distribution', 'derivative', 'computed', 'summation', 'efficiently', 'integration')
silver	('size', 'particles')
photographic	('particles',)
emulsion	('survival',)
bacteria	('time',)
disinfectants	('weight',)
blood	('weight', 'pressure')
pressure	('blood',)
sentences	('written', 'george')
george	('sentences', 'bernard')
bernard	('george',)
shaw	('log',)
log-series	('normalization', 'function', 'distribution')
von	('error', 'seggern', 'spiegel', 'seggern', 'parameter', 'mises', 'variance', 'mises')
seggern	('von', 'von', 'use')
map-airy	('distribution',)
airy	('function', 'map', 'distribution', 'distribution')
maxwell-boltzmann	('distribution', 'distribution')
speeds	('distribution', 'molecules')
equilibrium	('thermal', 'statistical')
mechanics	('defining',)
boltzmann	('defining',)
molecule	('speed', 'probability')
speed	('molecule',)
spiegel	('erf', 'von')
noncentrality	('distribution', 'parameter')
scheffe	('variable', 'bulgren')
bulgren	('scheffe',)
singly	('become', 'noncentral', 'analytically', 'noncentral', 'moment', 'noncentral')
mathematicians	('statistician', 'uniformly', 'because', 'word')
physicists	('distribution', 'gaussian')
flaring	('curved',)
social	('shape', 'feller')
switches	('equation', 'feller')
astronomical	('analysis', 'data')
converted	('distribution', 'standard')
changing	('distribution',)
fisher-behrens	('variable',)
extractions	('either', 'either')
astronomy	('dangerous',)
dangerous	('astronomy',)
attributes	('common', 'test')
invoke	('tendency', 'normal')
lippmann	('applicable',)
think	('because', 'mathematics;')
mathematics;	('think',)
amazing	('among', 'properties')
subtracting	('adding',)
normal!	('variance', 'normal')
formalism	('unbiased',)
half-infinite	('onto', 'interval')
extra	('transformation', 'factor')
promised	('chi-squared',)
owen	('distribution', 't', 'function', 'distribution', 't', 'function')
tetrachoric	('distribution', 'function', 'integral', 'function', 'integral', 'function')
widely	('less', 'encountered')
a014481	('large',)
a001147	('value',)
bagby	('due',)
hh	('integral', 'function')
alternate	('variate', 'derivation')
orthogonality	('obey',)
kronecker	('condition',)
v	('intermediate',)
iv	('case', 'type', 'distribution')
vi	('larger',)
ix-xii	('classes', 'discussed')
discussed	('ix-xii', 'pearson')
planck	('radiation', 'a133840', 'radiation')
radiation	('planck', 'function', 'function', 'planck', 'function')
a133838	('inflection',)
a133839	('oeis',)
a133840	('planck',)
a092678	(';', ';')
savageau	('problem', 'aksenov', 'aksenov', 'four', 's-systems', 'voit', 'aksenov', 's', 'distribution')
aksenov	('savageau', 'savageau', 'voit', 'savageau')
capable	('distribution', 'approximating')
approximating	('capable', 'many')
voit	('well', 'includes', 'savageau', 'aksenov')
s-systems	('theory', 'savageau')
messy	('computed', 'involves')
william	('published', 'gosset')
gosset	('william',)
employer	('guinness',)
guinness	('employer',)
breweries	('required',)
publish	('him', 'under')
pseudonym	('he',)
chose	('he', 'independent')
studenttdistribution	('distribution',)
multivariatetdistribution	('wolfram',)
student'	('student',)
b	('triangular',)
rectangular	('distribution', 'distribution', 'evenly-spaced', 'array')
exceeds	('sum', 'derbyshire')
derbyshire	('exceeds',)
a001048	('expected',)
a090138	('expected',)
a089087	('closed',)
a090611	('uniform',)
mises	('von', 'distribution', 'von', 'distribution')
lifetimes	('distribution',)
fatigue	('quantify',)
bean	('machine', 'quincunx')
labelled	('outcome', 'probability', 'probability', 'probability')
bernoullidistribution	('performance',)
building	('distribution', 'block')
curtailed	('trial', 'summarized')
a086117	('general',)
steinhaus	('case',)
grains	('number', 'board', 'results')
stirling	('use', 'polynomial')
ignore	('previous',)
characterized	('variable', 'ball', 'coefficient')
cochran	('theorem', 'theorem', 'theorem', 'distribution', 'theorem')
discreteuniformdistribution	('moment-generating',)
a086112	('discrete',)
quincunx	('board', 'bean')
device	('machine', 'statistical', 'front', 'covered')
english	('named', 'scientist')
scientist	('english', 'sir')
sir	('scientist', 'francis')
francis	('sir',)
upright	('galton', 'board')
evenly	('board', 'spaced')
nails	('spaced', 'half', 'arranged', 'viewing', 'funnel', 'only', 'potentially', 'bounce')
pegs	('driven',)
driven	('pegs', 'upper')
staggered	('arranged',)
evenly-spaced	('number', 'rectangular')
slots	('front', 'middle', 'number')
front	('slots', 'device')
glass	('covered', 'cover')
funnel	('edge', 'nails', 'located', 'dropped', 'over', 'opening')
poured	('diameter',)
located	('funnel', 'precisely')
nail	('central', 'second', 'point', 'surface')
uppermost	('onto', 'point')
kozlov	('surface', 'mitrofanova', 'dropped', 'mitrofanova')
mitrofanova	('kozlov', 'figure', 'kozlov', 'galton')
potentially	('nails', 'hit')
array	('triangular', 'rectangular')
bounce	('nails', 'right', 'ball', 'left')
hitting	('row', 'th')
peg	('th', 'left')
heaps	('height', 'ball', 'approximate')
sufficiently	('ball', 'large', 'change', 'small', 'change', 'small', 'sense')
setup	('including',)
elasticity	('including',)
restitution	('radius',)
transcendent	('first',)
a000629	('exponential',)
tossed	('coin', 'even')
successful	('selection', 'total', 'number', 'probability', 'probability', 'random')
pick-	('lottery',)
multichoose	('distribution',)
reserves	('work', 'term')
multinomial	('distribution', 'distribution', 'coefficient', 'covariance', 'distribution', 'distribution', 'coefficient')
pfeiffer	('pp', 'schum')
schum	('pfeiffer', 'sample')
transcendental	('leading', 'equation')
bell	('connection',)
dobiński	('kind',)
saslaw	('been', 'model')
galaxies	('clustering', 'number', 'volume', 'ratio')
gravitational	('ratio', 'energy')
energy	('gravitational', 'kinetic', 'kinetic', 'peculiar')
kinetic	('energy', 'energy')
peculiar	('energy',)
zeta	('distribution', 'distribution', 'riemann', 'hurwitz')
insurance	('modelling',)
modelling	('insurance', 'rare')
rare	('modelling',)
hurwitz	('deviation', 'zeta')
efficiently	('region', 'direct', 'computed', 'using')
evaluation	('appropriate', 'distribution')
extrema	('possible', 'region')
wish	('you', 'generate')
frechet	('satisfies',)
consequence	('useful', 'memoryless')
image	('range', 'under', 'range', 'domain', 'line')
precise	('domain',)
parked	('length', 'randomly')
cars	('number', 'fit', 'density', 'large', 'dvoretzky')
overlapping!	('satisfies',)
a050996	('inner',)
slowly	('integral', 'converging')
converging	('slowly', 'series')
renyi	('addition', 'strengthened', 'finch', 'parking')
strengthened	('renyi', 'dvoretzky')
dvoretzky	('strengthened', 'robbin', 'cars', 'solomon')
mannion	('robbin', 'oeis')
a086245	('numerical',)
blaisdell	('due', 'solomon')
palasti	('robbin', 'conjectured')
yet	('dimension', 'been')
disproven	('been', 'finch')
parking	('renyi',)
rimmer	('tail', 'nolan', 'parametrization', 'nolan')
nolan	('rimmer', 'described', 'rimmer', 'most')
stability	('index', 'characteristic')
stable	('economics', 'distribution')
surrogate	('data', 'spectra', 'general')
artificially	('data', 'generated')
mimic	('data', 'statistical')
isospectral	('data', 'surrogates')
surrogates	('isospectral', 'identical', 'scrambled', 'same')
spectra	('real', 'surrogate')
randomized	('data',)
scrambled	('phase', 'surrogates')
white	('data', 'noise')
addend	('probability',)
conversion	('variance', 'normal')
kallenberg	('distributed', 'six-line')
six-line	('kallenberg', 'proof')
cumbersome	('slightly', 'proof')
influenced	('data', 'many')
unrelated	('small', 'random')
lindeberg	('gaussian', 'condition', 'condition', 'feller', 'mean', 'sequence', 'theorem', 'condition', 'outcome', 'condition', 'feller', 'condition', 'p', 'condition', 'p', 'condition', 'satisfy', 'function', 'feller')
lyapunov	('theorem', 'condition', 'condition', 'central', 'hold', 'condition')
lindeberg-feller	('sufficient', 'central', 'condition', 'central')
strong	('theorem', 'law', 'arithmetic', 'law', 'number', 'law', 'obey', 'law', 'condition', 'law', 'feller', 'law', 'number', 'law', 'cf', 'law', 'number', 'law')
outrageous	('sample', 'thing')
thing	('outrageous', 'likely')
littlewood	('mosteller', 'event')
incredibly	('see', 'remarkable')
remarkable	('incredibly', 'diaconis')
frivolous	('coincidence', 'theorem', 'theorem', 'theorem', 'inequality', 'theorem')
le	('distribution', 'cam')
cam	('le', 'inequality')
zabell	('s', 'denotes', 'condition', 'feller')
cf	('strong',)
khinchin	('inequality', 'probability')
equipartition	('asymptotic', 'property')