Abstract
Let {Xnk} be an array of rowwise conditionally negative dependent random variables. Complete convergence of to 0 is obtained by using various conditions on the moments and conditional means.
Highlights
Introduction and PreliminariesConcepts of negative dependence have been useful in developing laws of large numbers
Chung-type laws of large numbers for arrays of independent random variables were developed by Taylor, Patterson and Bozorgnia in [2]
The major result of this paper shows that 1 n n k 1 X nk where complete convergence is defined (Hsu and Robbins [3]) by
Summary
Concepts of negative dependence have been useful in developing laws of large numbers (cf: Taylor, Patterson and Bozorgnia [1]). Chung-type laws of large numbers for arrays of independent random variables were developed by Taylor, Patterson and Bozorgnia in [2]. Definition 1.1 Two random variables X and Y are pairwise negatively dependent (ND) if. Where P Xi Bi denotes the conditional probability of the random variable X being in the Boral set Bi given the sub- field. Throughout this paper X nk :1 k n, n 1 will denote rowwise conditionally independent random variables such that EX nk 0 for all n and k. Of this paper, strong laws of large numbers for arrays of rowwise conditionally negatively dependent random variables
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