RELATIONSHIPS AMONG SOME NOTIONS OF BIVARIATE DEPENDENCE
BOEING SCIENTIFIC RESEARCH LABS SEATTLE WA MATHEMATICS RESEARCH LAB
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A random variable T is left tail decreasing in a random variable S if PT or t divides S or s is non-increasing in s for all t, and right tail increasing in S if PT 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. CovfS,T, gS,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.
- Statistics and Probability