From Archimedean to Liouville copulas

Alexander J. McNeil and Johanna Neslehová

Journal of Multivariate Analysis, 2010, vol. 101, issue 8, 1772-1790

Abstract: We use a recent characterization of the d-dimensional Archimedean copulas as the survival copulas of d-dimensional simplex distributions (McNeil and Neslehová (2009) [1]) 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 particular, a new formula for Kendall's tau is derived and a new dependence ordering for non-negative random variables is introduced which generalises the Laplace transform order. We then generalise the Archimedean copulas to obtain Liouville copulas, which are the survival copulas of Liouville distributions and which are non-exchangeable in general. We derive a formula for Kendall's tau of Liouville copulas in terms of the radial parts of the corresponding Liouville distributions.

Keywords: Archimedean; copula; Simplex; distribution; l1-norm; symmetric; distribution; Liouville; distribution; Kendall's; tau; Williamson; d-transform; Laplace; transform; Stochastic; ordering; Dependence; ordering; Stochastic; simulation (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (32)

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