GammaCHI: a package for the inversion and computation of the gamma and chi-square cumulative distribution functions (central and noncentral)

TL;DR

GammaCHI is a Fortran 90 package that offers reliable routines for computing and inverting gamma and chi-square distribution functions, including noncentral variants, with additional functions related to the gamma function.

Contribution

The package introduces accurate and reliable inversion routines for noncentral gamma distribution functions, which are novel compared to existing methods.

Findings

Provides routines for central and noncentral gamma functions

Includes inversion routines for noncentral distributions

Offers additional gamma-related functions like error and gamma functions

Abstract

A Fortran 90 module (GammaCHI) for computing and inverting the gamma and chi-square cumulative distribution functions (central and noncentral) is presented. The main novelty of this package are the reliable and accurate inversion routines for the noncentral cumulative distribution functions. Additionally, the package also provides routines for computing the gamma function, the error function and other functions related to the gamma function. The module includes the routines cdfgamC, invcdfgamC, cdfgamNC, invcdfgamNC, errorfunction, inverfc, gamma, loggam, gamstar and quotgamm for the computation of the central gamma distribution function (and its complementary function), the inversion of the central gamma distribution function, the computation of the noncentral gamma distribution function (and its complementary function), the inversion of the noncentral gamma distribution function, the computation of the error function and its complementary function, the inversion of the complementary error function, the computation of: the gamma function, the logarithm of the gamma function, the regulated gamma function and the ratio of two gamma functions, respectively.