An improved Bennett's inequality
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.
Arithmetic-geometric mean inequality, Bennett's inequality, Lambert W function, tail probability
Zheng, Songfeng. "An improved Bennett's inequality." Communications in Statistics-Theory and Methods 47, no. 17 (2018): 4152-4159.
Communications in Statistics - Theory and Methods