Journal of Probability and Statistics
Volume 2010 (2010), Article ID 764043, 17 pages
doi:10.1155/2010/764043
Research Article

Complete Convergence for Maximal Sums of Negatively Associated Random Variables

Victor M. Kruglov

Department of Statistics, Faculty of Computational Mathematics and Cybernetics, Moscow State University, Vorobyovy Gory, GSP-1, 119992, Moscow, Russia

Received 24 December 2009; Accepted 1 April 2010

Academic Editor: Mohammad Fraiwan Al-Saleh

Copyright © 2010 Victor M. Kruglov. 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

Necessary and sufficient conditions are given for the complete convergence of maximal sums of identically distributed negatively associated random variables. The conditions are expressed in terms of integrability of random variables. Proofs are based on new maximal inequalities for sums of bounded negatively associated random variables.