Modern Stochastics: Theory and Applications (Feb 2023)

Bernstein-type bounds for beta distribution

  • Maciej Skorski

DOI
https://doi.org/10.15559/23-vmsta223
Journal volume & issue
Vol. 10, no. 2
pp. 211 – 228

Abstract

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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.

Keywords