GammaCHI: a package for the inversion and computation of the gamma and chi-square cumulative distribution functions (central and noncentral)
This package provides accurate statistical computation tools for researchers and practitioners needing noncentral distribution inversions, but it is an incremental software contribution.
The paper presents GammaCHI, a Fortran 90 package for computing and inverting central and noncentral gamma and chi-square cumulative distribution functions. The key contribution is reliable and accurate inversion routines for noncentral distributions.
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.