A Note on Upper Tail Behavior of Liouville Copulas

A Note on Upper Tail Behavior of Liouville Copulas

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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 sara stedy stand aid 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 2000 bmw 528i front bumper given after the main results.