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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_0
Distribution 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 Pμ(x, y), Qμ(x, y) (lower than 10-150 ) are not admissible.
The admissible input parameter ranges for computing the noncentral cumulative gamma distribution functions Pμ(x, y), Qμ(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 Pμ(x, y), Qμ(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.