Various New Inequalities for Beta Distributions

TL;DR

This paper introduces new inequalities and approximations for beta distributions, including tail bounds, exponential inequalities, and Gaussian approximations, enhancing the understanding and analysis of beta distribution behaviors.

Contribution

It presents novel inequalities and approximation methods for beta distributions, expanding the tools available for probabilistic analysis and statistical inference.

Findings

Derived new tail inequalities for beta distributions

Established exponential inequalities of Hoeffding and Bernstein type

Provided Gaussian approximations for beta distributions

Abstract

This note provides some new inequalities and approximations for beta distributions, including tail inequalities, exponential inequalities of Hoeffding and Bernstein type, Gaussian inequalities and approximations.