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Statistical Analysis Module Documentation

This documentation provides an overview of the statistical analysis module, including its submodules, classes, and functions, featuring various utilities and functionalities for statistical analysis

Module: mdl_esti_md

This module includes functionalities related to model estimation.

Submodule: prediction_metrics

This submodule computes various prediction metrics.

  • compute_skew(arr): Computes skewness of an array.
  • compute_kurtosis(arr, residuals=None): Computes kurtosis of an array.
  • compute_aic_bic(dfr: int, n: int, llh: float, method: str = basic): Computes AIC (Akaike Information Criterion) and BIC (Bayesian Information Criterion).
  • Class PredictionMetrics: Computes various prediction metrics for regression models.
    • compute_mae(self): Computes Mean Absolute Error.
    • compute_log_likelihood(self, std_eval: float = None, debug=False, min_tol: float = True): Computes log-likelihood.
    • log_loss_flat(self, min_tol: float = None): Computes log loss.
    • log_loss(self, min_tol: float = True): Computes log loss.
    • get_confusion_matrix(self): Gets confusion matrix.
    • get_binary_accuracy(self): Gets binary accuracy.
    • get_precision_score(self): Gets precision score.
    • get_recall_score(self): Gets recall score.
    • get_f1_score(self): Gets F1 score.
    • get_binary_regression_res(self): Gets binary regression results.

Submodule: __init__

This submodule initializes the mdl_esti_md module.

Submodule: prediction_results

This submodule handles regression result data and computations.

  • Class RegressionResultData: Stores regression result data.
  • HPE_REGRESSION_FISHER_TEST(y: list, y_hat: list, nb_param: int, alpha: float = None): Performs regression Fisher test.
  • compute_linear_regression_results(crd: RegressionResultData, debug: bool = False): Computes linear regression results.
  • compute_logit_regression_results(crd: RegressionResultData, debug: bool = False): Computes logistic regression results.

Submodule: log_reg_example.py

This submodule provides an example implementation of logistic regression.

  • Class LogisticRegression: Implements logistic regression model.
  • ...

Submodule: hp_estimators_regression.py

This submodule provides functions for hypothesis testing in regression models.

  • sigmoid(z): Computes the sigmoid function.
  • log_loss(yp, y, min_tol: float = None): Computes log loss.
  • Class ComputeRegression: Computes regression coefficients and results.
  • ...

Submodule: model_estimator.py

This submodule contains functions for model estimation.

  • ME_Normal_dist(sample: list, alpha=None, debug=False): Estimates a normal distribution from a sample.
  • ME_Regression(x: list, y: list, degre: int, logit=False, fit_intercept=True, debug=False, alpha: float = 0.05, nb_iter: int = 100000, learning_rate: float = 0.1): Performs regression analysis.
  • ME_multiple_regression(X: list, y: list, logit=False, fit_intercept=True, debug=False, alpha: float = 0.05, nb_iter: int = 100000, learning_rate: float = 0.1): Performs multiple regression analysis.
  • ME_logistic_regression(X: list, y: list, debug=False, alpha=None): Performs logistic regression analysis.

Module: hyp_vali_md

This module handles hypothesis validation functionalities.

Submodule: constraints

This submodule provides constraint checking functions.

  • check_zero_to_one_constraint(*args): Checks if values are between zero and one.
  • check_or_get_alpha_for_hyph_test(alpha=None): Checks or retrieves alpha value for hypothesis testing.
  • check_or_get_cf_for_conf_inte(confidence=None): Checks or retrieves confidence level for confidence intervals.
  • check_hyp_min_sample(n: int, p: int = None): Checks minimum sample size for hypothesis testing.
  • check_hyp_min_samples(p1: float, p2: float, n1: int, n2: int, overall=False): Checks minimum sample sizes for hypothesis testing.

Submodule: hypothesis_validator

This submodule validates hypotheses.

  • check_residuals_centered(residuals: list, alpha=None): Checks if a list is centered.
  • check_coefficients_non_zero(list_coeffs: list, list_coeff_std: list, nb_obs: int, debug=False, alpha=None): Computes non-zero tests for each coefficient.
  • check_equal_var(*samples, alpha=COMMON_ALPHA_FOR_HYPH_TEST): Checks if samples have equal variance.
  • check_zero_to_one_constraint(*args): Checks if values are between zero and one.
  • check_or_get_alpha_for_hyph_test(alpha=None): Checks or retrieves alpha value for hypothesis testing.
  • check_or_get_cf_for_conf_inte(confidence=None): Checks or retrieves confidence level for confidence intervals.
  • check_hyp_min_sample(n: int, p: int = None): Checks minimum sample size for hypothesis testing.
  • check_hyp_min_samples(p1: float, p2: float, n1: int, n2: int, overall=False): Checks minimum sample sizes for hypothesis testing.

Module: conf_inte_md

This module handles confidence interval computations.

Submodule: confidence_interval

This submodule provides functions for computing confidence intervals.

  • IC_PROPORTION_ONE(sample_size: int, parameter: float, confidence: float = None, method: str = None): Computes confidence interval for one proportion.
  • IC_MEAN_ONE(sample: list, t_etoile=None, confidence: float = None): Computes confidence interval for one mean.
  • IC_PROPORTION_TWO(p1, p2, N1, N2, confidence: float = None): Computes confidence interval for the difference in proportions.
  • IC_MEAN_TWO_PAIR(sample1, sample2, t_etoile=None, confidence: float = None): Computes confidence interval for the difference in means for paired data.
  • IC_MEAN_TWO_NOTPAIR(sample1, sample2, pool=False, confidence: float = None): Computes confidence interval for the difference in means for non-paired data.

Submodule: ci_estimators

This submodule provides functions for estimating confidence intervals.

  • get_min_sample(moe: float, p=None, method=None, cf: float = None): Computes minimum sample size for a given margin of error.
  • CIE_ONE_PROPORTION(proportion, n, method, cf: float = None): Computes confidence interval for one proportion.
  • CIE_PROPORTION_TWO(p1, p2, n1, n2, cf: float = None): Computes confidence interval for the difference in proportions.
  • CIE_MEAN_ONE(n, mean_dist, std_sample, t_etoile=None, cf: float = None): Computes confidence interval for one mean.
  • CIE_MEAN_TWO(N1, N2, diff_mean, std_sample_1, std_sample_2, t_etoile=None, pool=False, cf: float = None): Computes confidence interval for the difference in means.

Module: hyp_testi_md

This module handles hypothesis testing functionalities.

Submodule: hp_estimators

This submodule provides functions for hypothesis testing estimations.

  • HPE_FROM_P_VALUE(tail: str = None, p_value=None, t_stat=None, p_hat=None, p0=None, std_stat_eval=None, alpha=None, test=z_test, ddl=0, onetail=False): Hypothesis testing from p-value.
  • HPE_PROPORTION_ONE(alpha, p0, proportion, n, tail=Tails.right): Hypothesis testing for one proportion.
  • HPE_PROPORTION_TW0(alpha, p1, p2, n1, n2, tail=Tails.middle, evcpp=False): Hypothesis testing for the difference in proportions between two populations.
  • HPE_MEAN_ONE(alpha, p0, mean_dist, n, std_sample, tail=Tails.right): Hypothesis testing for one mean.
  • HPE_MEAN_TWO_PAIRED(alpha, mean_diff_sample, n, std_diff_sample, tail=Tails.middle): Hypothesis testing for the difference in means between two paired samples.
  • HPE_MEAN_TWO_NOTPAIRED(alpha, diff_mean, N1, N2, std_sample_1, std_sample_2, pool=False, tail=Tails.middle): Hypothesis testing for the difference in means between two independent samples.
  • HPE_MEAN_MANY(*samples, alpha=None): Hypothesis testing for multiple means.

Submodule: hypothesis_testing

This submodule handles hypothesis testing.

  • HP_PROPORTION_ONE(sample_size: int, parameter: float, p0: float, alpha: float, symb=Tails.SUP_SYMB): Hypothesis testing for one proportion.
  • HP_MEAN_ONE(p0: float, alpha: float, sample: list, symb=Tails.SUP_SYMB): Hypothesis testing for one mean.
  • HP_PROPORTION_TWO(alpha, p1, p2, N1, N2, symb=Tails.NEQ_SYMB, evcpp=False): Hypothesis testing for the difference in proportions between two populations.
  • HP_MEAN_TWO_PAIR(alpha, sample1, sample2, symb=Tails.NEQ_SYMB): Hypothesis testing for the difference in means between two paired samples.
  • HP_MEAN_TWO_NOTPAIR(alpha, sample1, sample2, symb=Tails.NEQ_SYMB, pool=False): Hypothesis testing for the difference in means between two independent samples.

Module: utils_md

This module includes various utility functions for preprocessing and estimation.

Submodule: preprocessing

This submodule provides functions for preprocessing data.

  • clear_list(L: list) -> ndarray: Removes NaN values from a list.
  • clear_list_pair(L1, L2) -> Tuple[ndarray, ndarray]: Removes NaN values from two lists.
  • clear_mat_vec(A, y) -> Tuple[ndarray, ndarray]: Removes NaN values from a matrix and a corresponding vector.

Submodule: estimate_std

This submodule estimates standard deviation.

  • estimate_std(sample): Estimates standard deviation using (n-1) estimator.

Submodule: compute_ppf_and_p_value

This submodule computes probabilities and percentiles.

  • get_z_value(cf): Computes z-value based on confidence level.
  • get_t_value(cf, ddl): Computes t-value based on confidence level and degrees of freedom.
  • get_f_value(cf, ddl): Computes F-value based on confidence level and degrees of freedom.
  • get_p_value_from_tail(prob, tail, debug=False): Computes p-value based on cumulative distribution function.
  • get_p_value_z_test(Z: float, tail: str, debug=False): Computes p-value based on normal distribution.
  • get_p_value_t_test(Z: float, ddl, tail: str, debug: bool = False): Computes p-value based on Student's t-distribution.
  • get_p_value_f_test(Z: float, dfn: int, dfd: int, debug: bool = False): Computes p-value based on Fisher's F-distribution.
  • get_p_value(Z: float, tail: str, test: str, ddl: int = None, debug=False): Computes p-value based on specified distribution.

Submodule: constants

This submodule defines various constants used in hypothesis testing and confidence interval computations.

  • Class Confidence_data: Defines confidence data parameters.
  • Class Hypothesis_data: Defines hypothesis data parameters.
  • ...

Submodule: refactoring

This submodule provides utilities for refactoring code.

  • norm_tail(tail: str): Normalizes tail symbols.
  • get_tail_from_symb(symb: str): Converts symbol to tail.
  • ...