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Risks 2016, 4(4), 40;

A Note on Upper Tail Behavior of Liouville Copulas

Division of Statistics, Northern Illinois University, DeKalb, IL 60115, USA
Academic Editor: Qihe Tang
Received: 15 September 2016 / Revised: 4 October 2016 / Accepted: 3 November 2016 / Published: 8 November 2016
Full-Text   |   PDF [369 KB, uploaded 8 November 2016]


The family of Liouville copulas is defined as the survival copulas of multivariate Liouville distributions, and it covers the Archimedean copulas constructed by Williamson’s d-transform. Liouville copulas provide a very wide range of dependence ranging from positive to negative dependence in the upper tails, and they can be useful in modeling tail risks. In this article, we study the upper tail behavior of Liouville copulas through their upper tail orders. Tail orders of a more general scale mixture model that covers Liouville distributions is first derived, and then tail order functions and tail order density functions of Liouville copulas are derived. Concrete examples are given after the main results. View Full-Text
Keywords: tail order; tail order functions; tail order density; dirichlet distributions; scale mixtures tail order; tail order functions; tail order density; dirichlet distributions; scale mixtures
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Hua, L. A Note on Upper Tail Behavior of Liouville Copulas. Risks 2016, 4, 40.

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