Open Access
Translator Disclaimer
May, 1977 Association and Probability Inequalities
Kumar Jogdeo
Ann. Statist. 5(3): 495-504 (May, 1977). DOI: 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).

Citation

Download Citation

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

Information

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

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

Subjects:
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

JOURNAL ARTICLE
10 PAGES


SHARE
Vol.5 • No. 3 • May, 1977
Back to Top