Association and Probability Inequalities

Abstract

A "moving set inequality," a variant of the one considered by Anderson (1955) and Sherman (1955), is shown to yield a class of random variables whose absolute values are "associated." In particular, a model generated by "contaminated independence" forms the principal example. Further, it is proved that "concordant" functions of associated random variables are associated and then this result is applied to obtain a variety of probability inequalities related to multivariate normal and other distributions. These results generalize the ones obtained by Sidak (1967, 1968, 1971, 1973).