Sankhya: The Indian Journal of Statistics

2004, Volume 66, Pt. 4,  607-620

Dependence for Archimedean Copulas and Aging Properties of Their Generating Functionstions

By

Jean Av\'erous, Universit\'e Paul-Sabatier, France

Jean-Luc Dortet-Bernadet, Universit\'e Louis-Pasteur, France

SUMMARY. This paper details the correspondence between various dependence concepts and stochastic orderings for an Archimedean copula $C_{\phi}(x,y) = \phi^{-1} \{\phi(x)+\phi(y)\}$ and theaging properties of the corresponding life distribution $F_{\phi}(t) = 1 - \phi^{-1}(t)$. Various applications of the results are given.

 AMS (1991) subject classification}.Primary 62H05, 62H20 ; Secondary 62N05 ;

Key words and phrases. Archimedean copula, life distribution, dependence family, positive dependence ordering, reliability ordering.

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