Abstract
The sufficient and necessary conditions of complete moment convergence for negatively orthant dependent (NOD) random variables are obtained, which improve and extend the well-known results.
Highlights
1 Introduction The concept of complete convergence of a sequence of random variables was introduced by Hsu and Robbins [ ] as follows
When {Xn, n ≥ } is a sequence of i.i.d. random variables with mean zero, Chow [ ] first investigated the complete moment convergence, which is more exact than complete convergence
The aim of this paper is to extend and improve Theorem A to negatively orthant dependent (NOD) random variables
Summary
The concept of complete convergence of a sequence of random variables was introduced by Hsu and Robbins [ ] as follows. They proved that the sequence of arithmetic means of independent and identically distributed (i.i.d.) random variables converges completely to the expected value if the variance of the summands is finite This result has been generalized and extended in several directions, one can refer to [ – ] and so forth. (Asadian et al [ ]) For any v ≥ , there is a positive constant C(v) depending only on v such that if {Xn, n ≥ } is a sequence of NOD random variables with EXn = for every n ≥ , for all n ≥ , n v n. For any v ≥ , there is a positive constant C(v) depending only on v such that if {Xn, n ≥ } is a sequence of NOD random variables with EXn = for every n ≥ , for all n ≥ , j v.
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