Relationships Among Some Concepts of Bivariate Dependence

Esary, J. D.; Proschan, F.

Ann. Math. Statist., Tome 43 (1972) no. 6, p. 651-655 / Harvested from Project Euclid

Résumé

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 $g$.

Publié le : 1972-04-14
Classification:

@article{1177692646,
     author = {Esary, J. D. and Proschan, F.},
     title = {Relationships Among Some Concepts of Bivariate Dependence},
     journal = {Ann. Math. Statist.},
     volume = {43},
     number = {6},
     year = {1972},
     pages = { 651-655},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177692646}
}

Esary, J. D.; Proschan, F. Relationships Among Some Concepts of Bivariate Dependence. Ann. Math. Statist., Tome 43 (1972) no. 6, pp.  651-655. http://gdmltest.u-ga.fr/item/1177692646/