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May, 1977 Association and Probability Inequalities
Kumar Jogdeo
Ann. Statist. 5(3): 495-504 (May, 1977). DOI: 10.1214/aos/1176343846


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).


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Kumar Jogdeo. "Association and Probability Inequalities." Ann. Statist. 5 (3) 495 - 504, May, 1977.


Published: May, 1977
First available in Project Euclid: 12 April 2007

zbMATH: 0401.62028
MathSciNet: MR448703
Digital Object Identifier: 10.1214/aos/1176343846

Primary: 62H99
Secondary: 26A86

Keywords: associated random variables , concordant functions , Contaminated independence model , multivariate $t$ and $F$ distributions , multivariate normal , probability inequalities for rectangular sets and centrally symmetric convex sets , Wishart distribution

Rights: Copyright © 1977 Institute of Mathematical Statistics


Vol.5 • No. 3 • May, 1977
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