ON THE COMPLETE CONVERGENCE FOR ARRAYS OF ROWWISE EXTENDED NEGATIVELY DEPENDENT RANDOM VARIABLES

Abstract

Abstract. A general result for the complete convergence of arrays ofrowwise extended negatively dependent random variables is derived. Asits applications eight corollaries for complete convergence of weightedsums for arrays of rowwise extended negatively dependent random vari-ables are given, which extend the corresponding known results for inde-pendent case. 1. IntroductionThe concept of complete convergence of a sequence of random variables wasintroduced by Hsu and Robbins ([5]) as follows. A sequence {U n ,n≥ 1} ofrandom variables converges completely to the constant θifX ∞n=1 P{|U n −θ| >ǫ} 0.Moreover, they proved that the sequence of arithmetic means of independentidentically distribution (i.i.d.) random variables converges completely to theexpected value if the variance of the summands is finite. This result has beengeneralized and extended in several directions, see Gut ([3], [4]), Hu et al. ([7],[8]), Chen et al. ([2]), Sung ([14], [15], [17]), Zarei and Jabbari ([20]), Baek etal. ([1]). In particular, Sung ([14]) obtained the following two Theorems A andB.Theorem A. Let {X