Breaking update. It seriously changes parts of API. It adds new data types for
dealing with with estimates, confidence intervals, confidence levels and
p-value. Also API for statistical tests is changed.

Module `Statistis.Types`

now contains new data types for estimates,
upper/lower bounds, confidence level, and p-value.

`CL`

for representing confidence level`PValue`

for representing p-values`Estimate`

data type moved here from `Statistis.Resampling.Bootstrap`

and
now parametrized by type of error.`NormalError`

— represents normal error.`ConfInt`

— generic confidence interval`UpperLimit`

,`LowerLimit`

for upper/lower limits.

New API for statistical tests. Instead of simply return significant/not
significant it returns p-value, test statistics and distribution of test
statistics if it's available. Tests also return `Nothing`

instead of throwing
error if sample size is not sufficient. Fixes #25.

`Statistics.Tests.Types.TestType`

data type dropped

New smart constructors for distributions are added. They return `Nothing`

if
parameters are outside of allowed range.

Serialization instances (`Show/Read, Binary, ToJSON/FromJSON`

) for
distributions no longer allows to create data types with invalid
parameters. They will fail to parse. Cached values are not serialized either
so `Binary`

instances changed normal and F-distributions.

Encoding to JSON changed for Normal, F-distribution, and χ²
distributions. However data created using older statistics will be
successfully decoded.

Fixes #59.

Statistics.Resample.Bootstrap uses new data types for central estimates.

Function for calculation of confidence intervals for Poisson and binomial
distribution added in `Statistics.ConfidenceInt`

Tests of position now allow to ask whether first sample on average larger
than second, second larger than first or whether they differ significantly.
Affects Wilcoxon-T, Mann-Whitney-U, and Student-T tests.

API for bootstrap changed. New data types added.

Bug fixes for #74, #81, #83, #92, #94

`complCumulative`

added for many distributions.

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.

Discrete Fourie transform is 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