Asymptotic and numerical aspects of the noncentral chi-square distribution

DOI10.1016/0898-1221(93)90198-5zbMath0768.62013OpenAlexW2044008855MaRDI QIDQ2365952

Nico M. Temme

Publication date: 29 June 1993

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://ir.cwi.nl/pub/2307

zbMATH Keywords

error functionintegral representationasymptotic expansionsnormal distributionrecurrence relationsmodified Bessel functionincomplete gamma functionsnoncentral chi-square distributiongeneralized Marcum \(Q\)-function

Mathematics Subject Classification ID

Exact distribution theory in statistics (62E15) Probability distributions: general theory (60E05) Gamma, beta and polygamma functions (33B15) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Applications of hypergeometric functions (33C90) Probabilistic methods, stochastic differential equations (65C99)

Related Items (10)

New expression for CDF of \(\chi_{\nu}^{\prime 2}(\lambda)\) distribution and Marcum \(Q_1\) function ⋮ On new formulas for the cumulative distribution function of the noncentral chi-square distribution ⋮ Monotonicity properties and bounds for the chi-square and gamma distributions ⋮ Approximate arbitrage-free option pricing under the SABR model ⋮ The Asymptotic and Numerical Inversion of the MarcumQ-Function ⋮ Refined normal approximations for the central and noncentral chi-square distributions and some applications ⋮ CONSTANT ELASTICITY OF VARIANCE IN RANDOM TIME: A NEW STOCHASTIC VOLATILITY MODEL WITH PATH DEPENDENCE AND LEVERAGE EFFECT ⋮ Incomplete Exponential and Hypergeometric Functions with Applications to the Non Central χ²-Distribution ⋮ CDF of non-central \(\chi^2\) distribution revisited. Incomplete hypergeometric type functions approach ⋮ Algorithm 939

Cites Work

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• An error analysis of an algorithm for Marcum's Q-function
• A Double Integral Containing the Modified Bessel Function: Asymptotics and Computation
• Some integrals involving the<tex>Q_M</tex>function (Corresp.)
• Computation of the Noncentral Chi-Square Distribution*
• Computational Aspects of Three-Term Recurrence Relations
• Uniform Asymptotic Expansions for Saddle Point Integrals-Application to a Probability Distribution Occurring in Noise Theory

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