Monotonicity properties and bounds for the chi-square and gamma distributions

DOI10.1016/j.amc.2014.08.034zbMath1338.60042arXiv1406.6106OpenAlexW2153609623MaRDI QIDQ295215

Javier Segura

Publication date: 17 June 2016

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1406.6106

zbMATH Keywords

monotonicityconvexityboundsgamma distributioncumulative chi-square distributiongeneralized Marcum function

Mathematics Subject Classification ID

Probability distributions: general theory (60E05)

Related Items

A new type of sharp bounds for ratios of modified Bessel functions ⋮ \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 ⋮ Some new inequalities for beta distributions ⋮ A dynamic encryption-decryption scheme for replay attack detection in cyber-physical systems

Uses Software

• DLMF
• Algorithm 939

Cites Work

• Unnamed Item
• Bounds for ratios of modified Bessel functions and associated Turán-type inequalities
• Some inequalities for the Chi square distribution function and the exponential functions
• Tight bounds for the generalized Marcum \(Q\)-function
• Some inequalities for modified Bessel functions
• Estimation of the non-centrality parameter of a chi squared distribution
• Some inequalities of the incomplete gamma and related functions
• Asymptotic and numerical aspects of the noncentral chi-square distribution
• Inequalities for the generalized Marcum \(Q\)-function
• The Asymptotic and Numerical Inversion of the MarcumQ-Function
• Monotonicity results and inequalities for the gamma and incomplete gamma functions
• New Bounds for the Generalized Marcum $Q$-Function
• Algorithm 939
• Numerical Methods for Special Functions