Convergence And Strong Law Of Large Numbers For Weighted Sums Of Arrays Of NA Random Variables With Different Distributions

The concept of NA was introduced by Joag-Dev and Proschan in 1983.Random variables,X₁, X₂,…,X_n(n≥2)are said to be negatively associated if for every pair of disjoint subsets A₁,A₂of {1,2,…, n}whenever f₁ and f₂ are coordinatewise increasing and the covariance exists.A random sequences{X_i,i≥1} is called negatively associated if for arbitrary natural numbers are all negatively associated .Recently the limit theroy of NA random variables has been developed quickly on account of the broad application of NA random variables in many models (such as the reliability theroy,filtering theroy and mutivariate statistical analysis), and a great many conclusions consistent to independent situation have been obtained.But independent random sequences is just a kind of paticular case,negative association has one distinct adcantage over the other known types of nagetive dependence,increasing functions of disjoint sets of NA random variables are also NA, so it simulates per-fectly a varity of cases in application.This paper is composed of three chapters , chapter two and chapter three are main parts.In chapter two we mainly discuss convergence in probablity and complete convergence for weighted sums of arrays of NA random variables with different distributions under moment p≥2,at the same time we discuss the conditions of L^P convergence,the results we obtained are extended from sums of NA to weighted sums. In chapter three we establish the strong law of large numbers for weighted sums of NA random arrays with different distributions by using condition of exponent moment. The result presented in this paper is extended from the independent identically distributed case to the NA setting with different distributions.