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


CH Ndiaye
GS Lo

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 ex ≤ 1+x+(|x|/2) e|x| x ε R, in place of the following one: ex ≤ 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.


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print ISSN: 2316-090X