Archimedean copulas constitute an important class of dependence functions which enjoy considerable popularity in a number of practical applications. Recently, McNeil & Neslehova (2009) derived a characterization of d-variate Archimedean copulas as the survival copulas of d-dimensional simplex distributions. In this talk, I will present this result and show how it can be used to construct new Archimedean copula families, and to examine the relationship between their dependence properties and the radial parts of the corresponding simplex distributions. In addition, I will show how this characterization leads to a wide class of non-exchangeable copulas that includes the Archimedean copulas as a special case. The basic properties of this new class of dependence models, which are referred to as Liouville copulas, will be described.
Group for Research in Decision Analysis