Probability Inequalities for Set-Valued Negatively Orthant Dependent Random Variables

In this paper, we shall firstly give the definition of set-valued negatively orthant dependent random variables. And then prove some probability inequalities for set-valued negatively orthant dependent random variables. And the work is based on the results of (Petrov in Limit theorems of sequences of independent random variables, Clarendon Press, Oxford, 1995) and (Bozorgnia et al. in Limit theorems for ND random variables, 1993), and also is their extension.