A Note on Upper Tail Behavior of Liouville Copulas

Lei Hua
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Lei Hua: Division of Statistics, Northern Illinois University, DeKalb, IL 60115, USA

Risks, 2016, vol. 4, issue 4, 1-10

Abstract: 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.

Keywords: tail order; tail order functions; tail order density; dirichlet distributions; scale mixtures (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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