Association and Probability Inequalities
Open Access
- 1 May 1977
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Statistics
- Vol. 5 (3) , 495-504
- https://doi.org/10.1214/aos/1176343846
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).Keywords
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