We study a family of distributions generated from multiply monotone functions that includes a multivariate Pareto and, previously unidentified, exponential-Pareto distribution. We utilize an established link with Archimedean survival copulas to provide further examples, including a multivariate Weibull distribution, that may be used to fit light, or heavy-tailed phenomena, and which exhibit various forms of dependence, ranging from positive to negative. Because the model is intended for the study of joint lifetimes, we consider the effect of truncation and formulate properties required for a number of parameter estimation procedures based on moments and quantiles. For the quantile-based estimation procedure applied to the multivariate Weibull distribution, we also address the problem of optimal quantile selection.
Bibliographical noteFunding Information:
The authors would like to acknowledge the financial support of ARC Linkage [grant Project LP0883398] Managing Risk with Insurance and Superannuation as Individuals Age with industry partners PwC, APRA and the World Bank as well as the support of the Australian Research Council Centre of Excellence in Population Ageing Research [project number CE110001029].
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- Archimedean survival copulas
- Multiply monotone functions
- multivariate truncation
- Pareto distribution
- Weibull distribution
ASJC Scopus subject areas
- Statistics and Probability
- Economics and Econometrics
- Statistics, Probability and Uncertainty