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 is 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.

Additional Metadata
Keywords Gamma cumulative distribution function, chi-square cumulative distribution function, inversion of cumulative distribution functions, error function, complementary error function, gamma function, logarithm of the gamma function, regulated gamma function
THEME Software (theme 1), Information (theme 2)
Journal Computer Physics Communications
Citation
Gil, A, Segura, J, & Temme, N.M. (2015). GammaCHI: a package for the inversion and computation of the gamma and chi-square cumulative distribution functions (central and noncentral). Computer Physics Communications, (191), 132–139.