An improved Bennett's inequality

Songfeng Zheng

Communications in Statistics - Theory and Methods, 2018, vol. 47, issue 17, 4152-4159

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.

Date: 2018
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DOI: 10.1080/03610926.2017.1367818

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