A note on a new exponential bound for M-acceptable random variables

Abstract

We present a new exponential inequality as a generalization of that of Sung et al. Sung et al(2011) for $M$-acceptable random variables, and hence for extended negative ones. Our result is based on the simple real inequality $e^{x}\leq 1+x+(|x|/2)e^{|x|},x\in \mathbb{R}$, in place of the following one: $% e^{x}\leq 1+x+(x^{2}/2)e^{|x|},x\in \mathbb{R}$, used by many authors. We compare the given bound with former ones.