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

TL;DR

This paper introduces a new exponential inequality for M-acceptable random variables, generalizing previous bounds by employing a simpler inequality, and compares its effectiveness with existing bounds.

Contribution

It presents a novel exponential bound for M-acceptable random variables using a simpler inequality, extending previous results and broadening applicability.

Findings

New exponential inequality for M-acceptable variables

Comparison shows improved or comparable bounds

Applicable to extended negative random variables

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.