## Afrika Statistika

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

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

Cheikhna Hamallah Ndiaye and Gane Samb 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 $e^{x}\leq 1+x+(|x|/2)e^{|x|},x\in \mathbb{R}$, 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