Full description

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 0.10.0.0:
* The type classes @Mean@ and @Variance@ are split in two. This is
required for distributions which do not have finite variance or
mean.
* The @S.Sample.KernelDensity@ module 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 @S.Sample.KernelDensity.Simple@).
* Histogram computation is added, in @S.Sample.Histogram@.
* Forward and inverse discrete Fourier and cosine transforms are
added, in @S.Transform@.
* Root finding is added, in @S.Math.RootFinding@.
* The @complCumulative@ function is added to the @Distribution@
class in order to accurately assess probalities P(X>x) which are
used in one-tailed tests.
* A @stdDev@ function is added to the @Variance@ class for
distributions.
* The constructor @S.Distribution.normalDistr@ now takes standard
deviation instead of variance as its parameter.
* A bug in @S.Quantile.weightedAvg@ is 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 @mannWhitneyUCriticalValue@ is 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 @mannWhitneyUSignificant@ is fixed. If either sample was
larger than 20, it produced a completely incorrect answer.
* One- and two-tailed tests in @S.Tests.NonParametric@ are selected
with sum types instead of @Bool@.
* Test results returned as enumeration instead of @Bool@.
* Performance improvements for Mann-Whitney U and Wilcoxon tests.
* Module @S.Tests.NonParamtric@ is split into @S.Tests.MannWhitneyU@
and @S.Tests.WilcoxonT@
* @sortBy@ is added to @S.Function@.
* 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.
* The function @S.Function.create@ is removed. Use @generateM@ from
the @vector@ package instead.
* Function to perform approximate comparion of doubles is added to
@S.Function.Comparison@
* Regularized incomplete beta function and its inverse are added to
@S.Function@.