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The frailty and the archimedean structure of the general multivariate Pareto distributions
by Hsiaw-Chan Yeh

Vol. 2 No. 3 (2007) P.713~P.729

ABSTRACT

The mixture property of the general multivariate Pareto $\text{MP}^{(k)}$ distributions has been studied by Yeh (2004a). Arnold (1996) mentioned that any mixing distribution with support $(0,\infty)$ is a candidate for a frailty model. This fact drives Yeh to study the frailty structure of the $\text{MP}^{(k)}$ distributions. It is discerned that the $\text{MP}^{(k)}$ distributions is in the one-parameter $k$- variate Clayton family with $k$-variate Archimedean survival copulas and thus the $\text{MP}^{(k)}$ can be treated as a marginally specified multivariate distribution. Several properties of the $k$-variate survival copulas and the limiting special cases of the $\text{MP}^{(k)}$ Archimedean survival copulas are studied in this paper.

KEYWORDS
General multivariate Pareto distributions, $\text{MP}^{(k)}$, mixture, Laplace transform, frailty model, Archimedean generator, $k$-variate survival copulas, Clayton family, Kendall's $\gamma$

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