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April, 1972 Relationships Among Some Concepts of Bivariate Dependence
J. D. Esary, F. Proschan
Ann. Math. Statist. 43(2): 651-655 (April, 1972). DOI: 10.1214/aoms/1177692646


We consider some unresolved relationships among various notions of bivariate dependence. In particular we show that $P\lbrack T > t \mid S > s\rbrack \uparrow$ in $s$ (or alternately, $P\lbrack T \leqq t \mid S \leqq s\rbrack \downarrow$ in $s$) implies $S, T$ are associated, i.e. $\operatorname{Cov} \lbrack f(S, T), g(S, T)\rbrack \geqq 0$ for all non-decreasing $f$ and $g$.


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J. D. Esary. F. Proschan. "Relationships Among Some Concepts of Bivariate Dependence." Ann. Math. Statist. 43 (2) 651 - 655, April, 1972.


Published: April, 1972
First available in Project Euclid: 27 April 2007

zbMATH: 0263.62011
MathSciNet: MR298729
Digital Object Identifier: 10.1214/aoms/1177692646

Rights: Copyright © 1972 Institute of Mathematical Statistics

Vol.43 • No. 2 • April, 1972
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