GammaCHI: A package for the inversion and computation of the gamma and chi-square cumulative distribution functions (central and noncentral). New version announcement

Abstract

This is a revised and updated version of the package GammaCHI. The package includes routines for computing and inverting the gamma and chi-square cumulative distribution functions (central and noncentral). Additionally, the package also provides routines for computing the gamma function, the error function and other functions related to the gamma function (the logarithm of the gamma function, the regulated gamma function and the ratio of two gamma functions). In this new version, the range of computation of the inversion routine of the central gamma distribution function invcdfgamC(ichi,a,p,q,x,ierr) is extended; p or q input values close to the underflow limit are now allowed. New version program summaryProgram Title: GammaCHICPC Library link to program files:https://doi.org/10.17632/d2kwwvsyny.1Licensing provisions: GPLv2Programming language: Fortran 90Journal reference of previous version: Comput. Phys. Commun. 191 (2015) 132–139.Does the new version supersede the previous version?: YesReasons for the new version: With minor modifications of few of the functions included in the module GammaCHI, it is possible to enlarge the range of computation of the routine for the inversion of the central gamma distribution.Summary of revisions: The basic algorithms are unchanged. The range of computation of the routine for the inversion of the central gamma distribution function is extended in this new version. Specifically in the routine invcdfgamC(ichi,a,p,q,x,ierr) values of p or q close to the underflow limit are now allowed.Nature of problem: The computation and inversion of gamma and chi-square cumulative distribution functions (central and noncentral) as well as the computation of the error and gamma functions is needed in many problems of applied and mathematical physics. For example, central and noncentral gamma distributions are used in the analysis of signal detection in different physical scenarios such as optics or quantum detection.Solution method: Different methods of computation are used depending on the range of parameters: asymptotic expansions, quadrature methods, etc.