Probability Inequalities for Multivariate Distributions with Dependence Structures

Abstract

Abstract Let X 1, …, Xn be a sequence of random variables with a given positive or negative dependence structure. In this article we exploit the assumed dependence structure to construct a sequence of bounds for the P(Xi ε Ci ; i = 1, …, n), where Ci are infinite intervals of the same type. These bounds are superior to the well-known product bounds that are based solely on the marginal probabilities. Moreover, the new bounds can serve as respectable approximations for the P(Xi ε Ci ; i = 1, …, n).