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 ≤ 1+x+(|x|/2) e^|x| x ε R, in place of the following one: e^x ≤ 1+x+ (x²/2) e^{| x |},x ε R , used by many authors. We compare the given bound with former ones.

Key words: Exponential inequality; Convergence rate; Almost sure convergence; M- Acceptable random variables; Negatively associated random variables; Negatively dependent random variables; Extended Negatively dependent random variables; Laplace transform.