Title of article :
The Almost Sure Convergence for Weighted Sums of Linear Negatively Dependent Random Variables
Author/Authors :
Nili Sani، H.R. Department of Statistics - Faculty of Sciences - University of Birjand, Birjand, Iran , Amini، M. Department of Statistics - Faculty of Mathematical Sciences - Ferdowsi University of Mashhad, Mashhad, Iran , Bozorgnia2، A. Department of Statistics - Faculty of Mathematical Sciences - Ferdowsi University of Mashhad, Mashhad, Iran
Issue Information :
فصلنامه با شماره پیاپی سال 2009
Abstract :
In this paper, we generalize a theorem of Shao [12] by assuming that is a sequence of linear negatively dependent random variables. Also, we extend some theorems of Chao [6] and Thrum [14]. It is shown by an elementary method that for linear negatively dependent identically random variables with finite -th absolute moment the weighted sums converge to zero as where and is an array of real numbers. Moreover, we prove the almost sure convergence for weighted sums , when is a sequence of pairwise negative quadrant dependence stochastically bounded random variables under some suitable conditions on .
Abstract :
In this paper, we generalize a theorem of Shao [12] by assuming that is a sequence of linear negatively dependent random variables. Also, we extend some theorems of Chao [6] and Thrum [14]. It is shown by an elementary method that for linear negatively dependent identically random variables with finite -th absolute moment the weighted sums converge to zero as where and is an array of real numbers. Moreover, we prove the almost sure convergence for weighted sums , when is a sequence of pairwise negative quadrant dependence stochastically bounded random variables under some suitable conditions on .
Keywords :
Complete convergence , Negative association , Linear negatively dependent , Pairwise negatively dependent
Journal title :
Journal of Sciences
Journal title :
Journal of Sciences
