An improved Bennett's inequality

Abstract

This paper gives an improvement to Bennett's inequality for tail probability of sum of independent random variables, without imposing any additional condition. The improved version has a closed form expression. Using a refined arithmetic-geometric mean inequality, we further improve the obtained inequality. Numerical comparisons show that the proposed inequalities often improve the upper bound significantly in the far tail area, and these improvements get more prominent for larger sample size.

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.1080/03610926.2017.1367818

Keywords

Arithmetic-geometric mean inequality, Bennett's inequality, Lambert W function, tail probability

Publication Date

9-2-2018

Journal Title

Communications in Statistics - Theory and Methods

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