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.

翻译：本文给出了Beta分布的一些新不等式和近似结果，包括尾部不等式、Hoeffding型和Bernstein型指数不等式、高斯不等式及其近似。