Sufficient and necessary conditions of complete convergence for asymptotically negatively associated random variables

Abstract

Abstract In this investigation, some sufficient and necessary conditions of the complete convergence for weighted sums of asymptotically negatively associated (ANA, in short) random variables are presented without the assumption of identical distribution. As an application of the main results, the Marcinkiewicz–Zygmund type strong law of large numbers based on weighted sums of ANA cases is obtained. The results of this paper extend and generalize some well-known corresponding ones.

Keywords

• ANA random variables
• Complete convergence
• Weighed sums
• Equivalent conditions