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Relationships among some notions of bivariate dependence.

Author: J D Esary; F Proschan; BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH MATHEMATICS RESEARCH LAB.
Publisher: Ft. Belvoir Defense Technical Information Center JAN 1967.
Edition/Format:   Print book : English
Database:WorldCat
Summary:
A random variable T is left tail decreasing in a random variable S if P(T <or = t divides S <or = s) is non-increasing in s for all t, and right tail increasing in S if P(T> t divides S> s) is non-decreasing in s for all t. We show that either of these conditions implies that S, T are associated, i.e. Cov(f(S, T), g(S, T))> or = 0 for all pairs of functions f, g which are non-decreasing in each  Read more...
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Document Type: Book
All Authors / Contributors: J D Esary; F Proschan; BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH MATHEMATICS RESEARCH LAB.
OCLC Number: 227443538
Description: 11 pages

Abstract:

A random variable T is left tail decreasing in a random variable S if P(T <or = t divides S <or = s) is non-increasing in s for all t, and right tail increasing in S if P(T> t divides S> s) is non-decreasing in s for all t. We show that either of these conditions implies that S, T are associated, i.e. Cov(f(S, T), g(S, T))> or = 0 for all pairs of functions f, g which are non-decreasing in each argument. No two of these conditions for bivariate dependence are equivalent. Applications of these and other conditions for dependence in probability, statistics, and reliability theory are considered in Lehmann (1966) Ann. Math. Statist. and Esary, Proschan, and Walkup (1966) Boeing documents D1-82-0567, D1-82-0578. (Author).

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