Bernstein-type bounds for beta distribution

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Maciej Skorski

Published: 01 Jan 2023, Last Modified: 21 Apr 2026Modern Stochastics: Theory and ApplicationsEveryoneRevisionsCC BY-SA 4.0
Abstract: Publisher: VTeX - Solutions for Science Publishing, Journal: Modern Stochastics - Theory and Applications, Title: Bernstein-type bounds for beta distribution, Authors: Maciej Skorski , Abstract: This work obtains sharp closed-form exponential concentration inequalities of Bernstein type for the ubiquitous beta distribution, improving upon sub-Gaussian and sub-gamma bounds previously studied in this context. The proof leverages a novel handy recursion of order 2 for central moments of the beta distribution, obtained from the hypergeometric representations of moments; this recursion is useful for obtaining explicit expressions for central moments and various tail approximations.