statistics: A library of statistical types, data, and functions
This library provides a number of common functions and types useful in statistics. We focus on high performance, numerical robustness, and use of good algorithms. Where possible, we provide references to the statistical literature.
The library's facilities can be divided into four broad categories:
Working with widely used discrete and continuous probability distributions. (There are dozens of exotic distributions in use; we focus on the most common.)
Computing with sample data: quantile estimation, kernel density estimation, histograms, bootstrap methods, significance testing, and autocorrelation analysis.
Random variate generation under several different distributions.
Common statistical tests for significant differences between samples.
Changes in 0.10.1.0
Kolmogorov-Smirnov nonparametric test added.
Pearson's chi squared test added.
Type class for generating random variates for given distribution is added.
Statistics.Constantsare moved to the
math-functionspackage. They are still available but marked as deprecated.
Changed in 0.10.0.1
idctnow have type
Vector Double -> Vector Double
Changes in 0.10.0.0:
The type classes
Varianceare split in two. This is required for distributions which do not have finite variance or mean.
S.Sample.KernelDensitymodule has been renamed, and completely rewritten to be much more robust. The older module oversmoothed multi-modal data. (The older module is still available under the name
Histogram computation is added, in
Forward and inverse discrete Fourier and cosine transforms are added, in
Root finding is added, in
complCumulativefunction is added to the
Distributionclass in order to accurately assess probalities P(X>x) which are used in one-tailed tests.
stdDevfunction is added to the
Varianceclass for distributions.
S.Distribution.normalDistrnow takes standard deviation instead of variance as its parameter.
A bug in
S.Quantile.weightedAvgis fixed. It produced a wrong answer if a sample contained only one element.
Bugs in quantile estimations for chi-square and gamma distribution are fixed.
Integer overlow in
mannWhitneyUCriticalValueis fixed. It produced incorrect critical values for moderately large samples. Something around 20 for 32-bit machines and 40 for 64-bit ones.
A bug in
mannWhitneyUSignificantis fixed. If either sample was larger than 20, it produced a completely incorrect answer.
One- and two-tailed tests in
S.Tests.NonParametricare selected with sum types instead of
Test results returned as enumeration instead of
Performance improvements for Mann-Whitney U and Wilcoxon tests.
S.Tests.NonParamtricis split into
sortByis added to
Mean and variance for gamma distribution are fixed.
Much faster cumulative probablity functions for Poisson and hypergeometric distributions.
Better density functions for gamma and Poisson distributions.
Student-T, Fisher-Snedecor F-distributions and Cauchy-Lorentz distrbution are added.
S.Function.createis removed. Use
Function to perform approximate comparion of doubles is added to
Regularized incomplete beta function and its inverse are added to
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