文档介绍：Hindawi Publishing CorporationJournal of Probability and StatisticsVolume 2011, Article ID 202015,16pagesdoi: plete Convergence for WeightedSums of Sequences of Negatively DependentRandom VariablesQunying WuCollege of Science, Guilin University of Technology, Guilin 541004, ChinaCorrespondence should be addressed to Qunying Wu,******@ 30 September 2010; Accepted 21 January 2011Academic Editor: A. ThavaneswaranCopyrightq2011 Qunying Wu. This is an open access article distributed under the mons Attribution License, which permits unrestricted use, distribution, and reproduction inany medium, provided the original work is properly to the moment inequality of negatively dependent random variables pleteconvergence for weighted sums of sequences of negatively dependent random variables isdiscussed. As a result, complete convergence theorems for negatively dependent sequences ofrandom variables are . Introduction and LemmasDe?nition variablesXandYare said to be negatively dependent?ND?ifP?X≤x, Y≤y?≤P?X≤x?P?Y≤y???for allx, y∈R. A collection of random variables is said to be pairwise negatively dependent?PND?if every pair of random variables in the collection satis?es??.It is important to note that??implies thatP?X>x,Y>y?≤P?X>x?P?Y>y???for allx, y∈R. Moreover, it follows that??implies??, and, hence,??and??areequivalent. However,??and??are not equivalent for a collection of 3 or more randomvariables. Consequently, the following de?nition is needed to de?ne sequences of negativelydependent random Journal of Probability and StatisticsDe?nition random variablesX1,...,Xnare said to be negatively dependent?ND?if,for all realx1,...,xn,P??n?j?1?Xj≤xj???≤nj?1P?Xj≤xj?,P??n?j?1?Xj>xj???≤nj?1P?Xj>xj?.??An in?nite sequence of random variables{Xn;n≥1}is said to be ND if every ?nite subsetX1,...,Xnis ?nition