Computer Physics Communications Program LibraryPrograms in Physics & Physical Chemistry |

[Licence| Download | New Version Template] aevm_v1_0.tar.gz(83 Kbytes) | ||
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Manuscript Title: GammaCHI: a package for the inversion and computation of the gamma and chi-square cumulative distribution functions (central and noncentral) | ||

Authors: Amparo Gil, Javier Segura, Nico M. Temme | ||

Program title: Module GammaCHI | ||

Catalogue identifier: AEVM_v1_0Distribution format: tar.gz | ||

Journal reference: Comput. Phys. Commun. 191(2015)132 | ||

Programming language: Fortran 90. | ||

Computer: Any supporting a FORTRAN compiler. | ||

Operating system: Any supporting a FORTRAN compiler. | ||

RAM: a few MB | ||

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, Quotient of gamma functions. | ||

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 dierent 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(_{μ}x, y), Q(_{μ}x, y) (lower than 10^{-150} ) are not admissible.The admissible input parameter ranges for computing the noncentral cumulative gamma distribution functions P(_{μ}x, y), Q(_{μ}x, y) in standard IEEE double precision arithmetic are 0 ≤ x ≤ 10000, 0 ≤ y ≤ 10000, 0.5 ≤ μ ≤ 10000 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(_{μ}x, y), Q(_{μ}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. |

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