On new formulas for the cumulative distribution function of the noncentral chi-square distribution

DOI10.1007/s00009-017-0874-1zbMath1370.62009OpenAlexW2593720936MaRDI QIDQ2363003

Dragana Jankov Maširević

Publication date: 12 July 2017

Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00009-017-0874-1

zbMATH Keywords

modified Bessel functionsNeumann seriesgeneralized incomplete gamma functionnoncentral chi-square distributionleaky aquifer function

Mathematics Subject Classification ID

Exact distribution theory in statistics (62E15) Other functions defined by series and integrals (33E20) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10)

Related Items (5)

New expression for CDF of \(\chi_{\nu}^{\prime 2}(\lambda)\) distribution and Marcum \(Q_1\) function ⋮ Observations on the McKay \(I_\nu\) Bessel distribution ⋮ Refined normal approximations for the central and noncentral chi-square distributions and some applications ⋮ Bounds for confluent Horn function Φ2 deduced by McKay Iν Bessel law ⋮ CDF of non-central \(\chi^2\) distribution revisited. Incomplete hypergeometric type functions approach

Uses Software

• DLMF
• Algorithm 644

Cites Work

• New summations of Neumann series of modified Bessel functions
• The generalized incomplete gamma function as sum over modified Bessel functions of the first kind
• Properties of the probability density function of the non-central chi-squared distribution
• Modified Bessel functions and their applications in probability and statistics
• On the Mellin transform of products of Bessel and generalized hypergeometric functions
• Generalized series of Bessel functions
• Generalized incomplete gamma functions with applications
• Asymptotic and numerical aspects of the noncentral chi-square distribution
• Incomplete Bessel, generalized incomplete gamma, or leaky aquifer functions
• The special functions and their approximations. Vol. I, II
• On some properties of the MarcumQfunction
• Integral representations for Neumann-type series of Bessel functions $I_{𝜈},$ $Y_{𝜈}$ and $K_{𝜈}$
• The generalized Marcum $Q-$function: an orthogonal polynomial approach
• Asymptotic Methods for Integrals
• On the Computation of Modified Bessel Function Ratios
• Algorithm 644
• Approximations to the non-central chi-square distribution
• Theory of Incomplete Cylindrical Functions and their Applications
• A Note on the Convergence of KAMPÉ DE FÉRIET's Double Hypergeometric Series
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