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

Gane Samb Lo; Cheikhna Hamallah Ndiaye

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arXiv · 1405.5508

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

Gane Samb Lo·Cheikhna Hamallah Ndiaye

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Abstract

We present a new exponential inequality as a generalization of that of Sung \textit{et al.} \cite{sun2011} 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.

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Gane Samb Lo, Cheikhna Hamallah Ndiaye. 2014-05-21. A note on a new exponential bound for M-acceptable random variables. https://arxiv.org/abs/1405.5508

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