Abstract
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 $g$.
Citation
J. D. Esary. F. Proschan. "Relationships Among Some Concepts of Bivariate Dependence." Ann. Math. Statist. 43 (2) 651 - 655, April, 1972. https://doi.org/10.1214/aoms/1177692646
Information
