Normalized incomplete beta function: log-concavity in parameters and other properties

DOI10.1007/s10958-016-2958-zzbMath1358.33001arXiv1509.05120OpenAlexW2964096725MaRDI QIDQ2520418

Dmitriĭ Borisovich Karp

Publication date: 13 December 2016

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.05120

zbMATH Keywords

incomplete beta functionTurán determinantslogarithmic concavity/convexity

Mathematics Subject Classification ID

Characterization and structure theory of statistical distributions (62E10) Convexity of real functions of several variables, generalizations (26B25) Exponential and trigonometric functions (33B10)

Related Items (6)

Inequalities for series in \(q\)-shifted factorials and \(q\)-gamma functions ⋮ Log concavity preservation by beta operator based on probability tools ⋮ Hadamard products in weighted Bergman spaces ⋮ Log-concavity and Turán-type inequalities for the generalized hypergeometric function ⋮ Logarithmic concavity of the inverse incomplete beta function with respect to the first parameter ⋮ A new identity for the sum of products of the generalized hypergeometric functions

Uses Software

• BayesDA

Cites Work

• Functional inequalities for the incomplete gamma function
• Log-convexity and log-concavity of hypergeometric-like functions
• Completely monotonic functions involving divided differences of the di- and tri-gamma functions and some applications
• Inequalities for the chi square distribution function
• Log-convexity and log-concavity for series in gamma ratios and applications
• Logarithmic concavity of series in gamma ratios
• Some People Have All the Luck
• On Gamma Function Inequalities
• Distribution functions and log-concavity
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