Statistical functions in Common Lisp
Common Lisp
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Statistical functions in Common Lisp. Version 1.01 July 27, 2001

Documentation from lhstats.lisp:

This comes in large part from Larry Hunter but has been significantly augmented by Jeff Shrager, partly from his own stats libraries, and partly from open source stuff borrowed from around the web. Citations and acknowledgements are given where possible.

Patches welcome (preferably via pull requests at

Larry Hunter’s Code

Statistical functions in Common Lisp. Version 1.01 July 27, 2001

This code is copyright (c) 2000 by Larry Hunter ( except where otherwise noted.

Thanks to Paul Cohen for the original CLASP package. Thanks also to bug reports from Rob St. Amant.

This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA

The formulas and methods used are largely taken from Bernard Rosner, “Fundamentals of Biostatistics,” 5th edition. “Rosner x” is a page number. Some numeric functions were taken from CLASP, a 1994 common lisp package that implemented some of the statistical functions from “Numeric recipes in C” For CLASP functions, see copyright notice below.

These abreviations used in function and variable names:

ciconfidence interval
cdfcumulative density function
gegreater than or equal to
leless than or equal to
pdfprobability density function
sdstandard deviation
rxcrows by columns
ssesample size estimate

Functions provided

Descriptive statistics

Mean, median, mode, geometric mean, range, percentile, variance, standard-deviation (sd), coefficient-of-variation, standard-error-of-the-mean

Distributional functions

Poisson & Binomial

binomial-probability, binomial-cumulative-probability, binomial-ge-probability, poisson-probability, poisson-cumulative-probability, poisson-ge-probability, Normal normal-pdf, convert-to-standard-normal, phi, z, t-distribution, chi-square, chi-square-cdf

Confidence Intervals

binomial-probability-ci, poisson-mu-ci, normal-mean-ci, normal-mean-ci-on-sequences, normal-variance-ci, normal-variance-ci-on-sequence, normal-sd-ci

Hypothesis tests (parametric)

z-test, z-test-on-sequence, t-test-one-sample, t-test-one-sample-on-sequence, t-test-paired, t-test-paired-on-sequences, t-test-two-sample, t-test-two-sample-on-sequences, chi-square-test-one-sample, f-test, binomial-test-one-sample, binomial-test-two-sample, fisher-exact-test, mcnemars-test, poisson-test-one-sample

Hypothesis tests (non-parametric)

sign-test, sign-test-on-sequence, wilcoxon-signed-rank-test, chi-square-test-rxc, chi-square-test-for-trend

Sample size estimates

t-test-one-sample-sse, t-test-two-sample-sse t-test-paired-sse, binomial-test-one-sample-sse, binomial-test-two-sample-sse, binomial-test-paired-sse, correlation-sse

Correlation and Regression

linear-regression, correlation-coefficient, correlation-test-two-sample, spearman-rank-correlation

Significance test functions

t-significance, f-significance (chi square significance is calculated from chi-square-cdf in various ways depending on the problem).


random-sample, random-pick, bin-and-count, fishers-z-transform, mean-sd-n, square, choose, permutations, round-float