From Archimedean to Liouville copulas

Alexander J. McNeil, Johanna Nešlehová*

*Korrespondierende*r Autor*in für diese Arbeit

Publikation: Wissenschaftliche FachzeitschriftOriginalbeitrag in FachzeitschriftBegutachtung

Abstract

We use a recent characterization of the d-dimensional Archimedean copulas as the survival copulas of d-dimensional simplex distributions (McNeil and Nešlehová (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.

OriginalspracheEnglisch
Seiten (von - bis)1772-1790
Seitenumfang19
FachzeitschriftJournal of Multivariate Analysis
Jahrgang101
Ausgabenummer8
DOIs
PublikationsstatusVeröffentlicht - Sept. 2010
Extern publiziertJa

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