COMPLETE CONVERGENCE FOR WEIGHTED SUMS OF NEGATIVELY SUPERADDITIVE DEPENDENT RANDOM VARIABLES

Abstract

In this paper we obtain complete convergences for weighted sums of negatively superadditive dependent random variables. These results generalize the corresponding ones for negatively associated random variables. P 1 i=1 P(jXi i Cj > †) 0. By Borel-Cantelli lemma, this implies that Xn ! C almost surely (a.s.). The converse is true if fXn;n ‚ 1g are independent. Hsu and Robbins (1947) also proved that the sequence of arithmetic means of i.i.d. random variables converges completely to the expected value if the variance of the summands is flnite. The complete convergence plays an important role in probability limit theory and mathematical statistics, especially, in establishing the con- vergence rate. A new kind of dependence structure called negatively superadditive dependence was introduced by Hu (2000) based on the class of superad- ditive functions. Superadditive structure functions have important relia- bility interpretations, which describe whether a system is more series-like