\texttt{GammaCHI}: a package for the inversion and computation of the gamma and chi-square cumulative distribution functions (central and noncentral)

DOI10.1016/j.cpc.2015.01.004zbMath1345.62012arXiv1501.01578OpenAlexW2151310023MaRDI QIDQ311830

Amparo Gil, Nico M. Temme, Javier Segura

Publication date: 13 September 2016

Published in: Computer Physics Communications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.01578

zbMATH Keywords

computation and inversion of noncentral gamma/chi-square cumulative distribution functionserror and gamma functions

Mathematics Subject Classification ID

Related Items (10)

Sharp bounds for cumulative distribution functions ⋮ A new asymptotic representation and inversion method for the Student's t distribution ⋮ Universal recurrence algorithm for computing Nuttall, generalized Marcum and incomplete Toronto functions and moments of a noncentral \(\chi^{2}\) random variable ⋮ The Schwarzian-Newton method for solving nonlinear equations, with applications ⋮ Asymptotic inversion of the binomial and negative binomial cumulative distribution functions ⋮ Conical: an extended module for computing a numerically satisfactory pair of solutions of the differential equation for conical functions ⋮ Efficient algorithms for the inversion of the cumulative central beta distribution ⋮ On the computation and inversion of the cumulative noncentral beta distribution function ⋮ Fast and reliable high-accuracy computation of Gauss-Jacobi quadrature ⋮ GammaCHI

Uses Software

• DLMF
• ncg
• Algorithm 939

Cites Work

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• Monotonicity properties and bounds for the chi-square and gamma distributions
• Uniform asymptotics for the incomplete gamma functions starting from negative values of the parameters
• Computing the noncentral gamma distribution, its inverse and the noncentrality parameter
• The Asymptotic and Numerical Inversion of the MarcumQ-Function
• The Schwarzian-Newton method for solving nonlinear equations, with applications
• The Asymptotic Inversion of Certain Cumulative Distribution Functions
• Computation of the Noncentral Gamma Distribution
• Efficient and Accurate Algorithms for the Computation and Inversion of the Incomplete Gamma Function Ratios
• Algorithm 939
• Numerical Methods for Special Functions
• On the Calculation of the Inverse of the Error Function.
• Rational Chebyshev Approximations for the Error Function

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