English

Bernstein-Type Bounds for Beta Distribution

Probability 2024-10-21 v5 Statistics Theory Applications Statistics Theory

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.

Keywords

Cite

@article{arxiv.2101.02094,
  title  = {Bernstein-Type Bounds for Beta Distribution},
  author = {Maciej Skorski},
  journal= {arXiv preprint arXiv:2101.02094},
  year   = {2024}
}

Comments

major revision - fixed a mistake in the proof

R2 v1 2026-06-23T21:50:38.637Z