Afrika Statistika

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

Cheikhna Hamallah Ndiaye and Gane Samb LO

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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.

Article information

Source
Afr. Stat., Volume 8, Number 1 (2013), 575-581.

Dates
First available in Project Euclid: 5 January 2014

Permanent link to this document
https://projecteuclid.org/euclid.as/1388953759

Digital Object Identifier
doi:10.4314/afst.v8i1.6

Mathematical Reviews number (MathSciNet)
MR3161754

Zentralblatt MATH identifier
1283.60050

Subjects
Primary: 60F15: Strong theorems 62G20: Asymptotic properties

Keywords
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

Citation

Ndiaye, Cheikhna Hamallah; LO, Gane Samb. A note on a new exponential bound for M-acceptable random variables. Afr. Stat. 8 (2013), no. 1, 575--581. doi:10.4314/afst.v8i1.6. https://projecteuclid.org/euclid.as/1388953759


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