Bernstein-Type Bounds for Beta Distribution
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- January 2021
- DOI:
- 10.48550/arXiv.2101.02094
- arXiv:
- arXiv:2101.02094
- Bibcode:
- 2021arXiv210102094S
- Keywords:
-
- Mathematics - Probability;
- Mathematics - Statistics Theory;
- Statistics - Applications;
- 60E05;
- G.3
- E-Print:
- major revision - fixed a mistake in the proof