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

DOI: 
10.1016/j.cpc.2015.01.004
Publication date: 
01/06/2015
Main author: 
Gil, Amparo
IAA authors: 
Temme, Nico M.
Authors: 
Gil, Amparo; Segura, Javier; Temme, Nico M.
Journal: 
COMPUTER PHYSICS COMMUNICATIONS
Publication type: 
Article
Volume: 
191
Pages: 
132-139
Number: 
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 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. Program summary Program title: Module GammaCHI Catalogue identifier: AEVM_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEVM_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 7653 No. of bytes in distributed program, including test data, etc.: 85283 Distribution format: tar.gz Programming language: Fortran 90. Computer: Any supporting a FORTRAN compiler. Operating system: Any supporting a FORTRAN compiler. RAM: a few MB Classification: 4.7. 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. Solution method: The algorithms use different methods of computation depending on the range of parameters: asymptotic expansions, quadrature methods, etc. Restrictions: In the inversion of the central gamma/chi-square distribution functions, very small input function values P-mu(x, y), Q(mu)(x, y) (lower than 10(-150)) are not admissible. The admissible input parameter ranges for computing the noncentral cumulative gamma distribution functions P-mu(x, y), Q(mu)(x, y) in standard IEEE double precision arithmetic are 0 <= x <= 10,000, 0 <= y <= 10,000, 0.5 <= mu <= 10,000 and the related parameter ranges for the noncentral chi-square cumulative distribution function. In the inversion of the noncentral gamma/chi-square distribution functions, very small input function values P-mu(x, y), Q(mu)(x, y) (lower than 10(-25) and 10(-35), respectively) are not admissible. Running time: It varies depending on the function and the parameter range. The test provided takes milliseconds. (C) 2015 Elsevier B.V. All rights reserved.
Database: 
WOK
Keywords: 
Computation and inversion of noncentral gamma/chi-square cumulative distribution functions; Error and gamma functions