Algorithm 939

DOI10.1145/2591004zbMath1322.65046arXiv1311.0681OpenAlexW1967855472WikidataQ113310302 ScholiaQ113310302MaRDI QIDQ5177206

Javier Segura, Amparo Gil, Nico M. Temme

Publication date: 10 March 2015

Published in: ACM Transactions on Mathematical Software (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.0681

zbMATH Keywords

noncentral chi-square distributionMarcum \(Q\)-function

Mathematics Subject Classification ID

Computation of special functions and constants, construction of tables (65D20) Other functions defined by series and integrals (33E20)

Related Items (8)

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 Asymptotic and Numerical Inversion of the MarcumQ-Function ⋮ Universal recurrence algorithm for computing Nuttall, generalized Marcum and incomplete Toronto functions and moments of a noncentral \(\chi^{2}\) random variable ⋮ Some inverse Laplace transforms that contain the Marcum Q function and an expanded property of the Marcum Q function ⋮ Algorithm 939 ⋮ Asymptotic and numerical aspects of the generalized Marcum function of the second kind

Uses Software

• DLMF

Cites Work

• Evaluating the noncentral chi-square distribution for the Cox-Ingersoll-Ross process
• Asymptotic and numerical aspects of the noncentral chi-square distribution
• Recursive Computation of Certain Integrals
• A Double Integral Containing the Modified Bessel Function: Asymptotics and Computation
• The calculation of the probability of detection and the generalized Marcum Q-function
• On the Computation of Non-Central Chi-Square Distribution Function
• Monotonicity results and inequalities for the gamma and incomplete gamma functions
• Algorithm for calculating the noncentral chi-square distribution
• Computation of the Noncentral Gamma Distribution
• Efficient and Accurate Algorithms for the Computation and Inversion of the Incomplete Gamma Function Ratios
• Numerical Methods for Special Functions
• Uniform asymptotic expansions of integrals with stationary point near algebraic singularity
• Uniform Asymptotic Expansions for Saddle Point Integrals-Application to a Probability Distribution Occurring in Noise Theory

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