About the Math Toolkit

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### About the Math Toolkit

This library is divided into three interconnected parts:

##### Statistical Distributions

Provides a reasonably comprehensive set of statistical distributions, upon which higher level statistical tests can be built.

The initial focus is on the central univariate distributions. Both continuous (like normal & Fisher) and discrete (like binomial & Poisson) distributions are provided.

A comprehensive tutorial is provided, along with a series of worked examples illustrating how the library is used to conduct statistical tests.

##### Mathematical Special Functions

Provides a small number of high quality special functions, initially these were concentrated on functions used in statistical applications along with those in the Technical Report on C++ Library Extensions.

The function families currently implemented are the gamma, beta & erf functions along with the incomplete gamma and beta functions (four variants of each) and all the possible inverses of these, plus digamma, various factorial functions, Bessel functions, elliptic integrals, sinus cardinals (along with their hyperbolic variants), inverse hyperbolic functions, Legrendre/Laguerre/Hermite polynomials and various special power and logarithmic functions.

All the implementations are fully generic and support the use of arbitrary "real-number" types, although they are optimised for use with types with known-about significand (or mantissa) sizes: typically `float`, `double` or `long double`.

##### Implementation Toolkit

Provides many of the tools required to implement mathematical special functions: hopefully the presence of these will encourage other authors to contribute more special function implementations in the future. These tools are currently considered experimental: they are "exposed implementation details" whose interfaces and/or implementations may change.

There are helpers for the evaluation of infinite series, continued fractions and rational approximations.

There is a fairly comprehensive set of root finding and function minimisation algorithms: the root finding algorithms are both with and without derivative support.

A Remez algorithm implementation allows for the locating of minimax rational approximations.

There are also (experimental) classes for the manipulation of polynomials, for testing a special function against tabulated test data, and for the rapid generation of test data and/or data for output to an external graphing application.