We consider some unresolved relationships among various notions of bivariate dependence. In particular we show that P T > t S > s ↑ in s (or alternately, P T t S s ↓ in s) implies $S, T$ are associated, i.e. Cov f(S, T), g(S, T) 0 for all non-decreasing f and g.
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Esary et al. (1972) studied this question.
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