On Complete Convergence Of Weighted Sums For Arrays Of Rowwise NOD Random Variables

Theory of probability is a science of quantitatively studying regularity of random phenomena, which is applied in natural science, technological science, social science and managerial science etc extensively. Hence, it has been developing rapidly since 1930’s and many new branches have merged from now to then. Limit theory is one of the parts and also an important theoretical basis of science of Probability theory and Statistics. In order to enforce application importance of limit theory, researchers are committed to weakening the restriction of independence in recent years. Limit Theory of dependent sequences is applied widely in Penetration the-ory, Complexity of the system and other fields. After that, many statis-ticians discuss the convergence properties of all types of mixing sequence. The concept of negative association(NA) random variable was introduced by Joag-Dev and Proschan in the eighties at last century. Then, number-s of results on the NOD sequences were getted, which are same as i.i.d random variable. These results are widely useful for the study on random process.In this paper, we discuss the moment inequalities and Kolmogorov-type inequality for sequences of NOD random variables, and complete convergence of weighted sums for arrays of rowwise NOD random variables. It is divided into three chapters as follows:In the first chapter, research background of this paper is introduced briefly. Definitions of sequences of NOD random variables studied in this paper and notion of complete convergence are given in this chapter. More-over, we establish the moment inequality and Kolmogorov-type inequality for sequences of NOD random variables.In the second chapter, by applying moment inequality and truncation methods, some sufficient conditions of complete convergence of weighted sums for arrays of rowwise NOD random variables are established. The results improves upon Theorem 1.5 of Kuczmaszews. Moreover, From our results, we see that condition (ii) in Theorem 1.5 of Kuczmaszewska’23’ is unnecessary.In the third chapter, by using the sufficient conditions of the complete convergence for arrays of rowwise NOD random variables in chapter two, some applications are given. The results of Qiu et al, Wu and Baek et al.are promoted and improved.