Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 649427, 7 pages
doi:10.1155/2009/649427
Research Article

An Exponential Inequality for Negatively Associated Random Variables

Soo Hak Sung

Department of Applied Mathematics, Pai Chai University, Taejon 302-735, South Korea

Received 15 October 2008; Revised 16 February 2009; Accepted 7 May 2009

Academic Editor: Jewgeni Dshalalow

Copyright © 2009 Soo Hak Sung. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

An exponential inequality is established for identically distributed negatively associated random variables which have the finite Laplace transforms. The inequality improves the results of Kim and Kim (2007), Nooghabi and Azarnoosh (2009), and Xing et al. (2009). We also obtain the convergence rate O(1)n1/2(log⁡n)−1/2 for the strong law of large numbers, which improves the corresponding ones of Kim and Kim, Nooghabi and Azarnoosh, and Xing et al.