2007 / September Volume 2 No.3
The frailty and the archimedean structure of the general multivariate Pareto distributions
| Published Date |
2007 / September
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|---|---|
| Title | The frailty and the archimedean structure of the general multivariate Pareto distributions |
| Author | |
| Keyword |
General multivariate Pareto distributions, M$P^(k)$, mixture, Laplace transform, fraity model, Archimedean generator, $k$-variate survival copulas, Clayton family, Kendall's $\tau$, 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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| Pagination | 713-729 |
| 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.
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| Received |
2006-08-02
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