The Asymptotic and Numerical Inversion of the MarcumQ-Function

DOI10.1111/SAPM.12050zbMath1302.33020arXiv1404.0302OpenAlexW1887684582MaRDI QIDQ2925248

Amparo Gil, Javier Segura, Nico M. Temme

Publication date: 21 October 2014

Published in: Studies in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1404.0302

zbMATH Keywords

generalized Marcum \(Q\)-functiongeneralized Marcum functionscomplementary Marcum \(P\)-functionnoncentral gammareliability of the asymptotic approximations

Mathematics Subject Classification ID

Numerical computation of solutions to single equations (65H05) Other functions defined by series and integrals (33E20) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10)

Related Items (4)

Monotonicity properties and bounds for the chi-square and gamma distributions ⋮ \texttt{GammaCHI}: a package for the inversion and computation of the gamma and chi-square cumulative distribution functions (central and noncentral) ⋮ Sharp bounds for cumulative distribution functions ⋮ The generalized Marcum function of the second kind: monotonicity patterns and tight bounds

Uses Software

• Algorithm 939

Cites Work

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• Monotonicity properties and bounds for the chi-square and gamma distributions
• Bounds for ratios of modified Bessel functions and associated Turán-type inequalities
• An efficient algorithm for computing quantiles of the noncentral chi-squared distribution.
• Asymptotic and numerical aspects of the noncentral chi-square distribution
• The Asymptotic Inversion of Certain Cumulative Distribution Functions
• Asymptotic Inversion of Incomplete Gamma 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

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