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From Archimedean to Liouville copulas

  • McNeil, Alexander J.
  • Neslehová, Johanna
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    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.

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    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 101 (2010)
    Issue (Month): 8 (September)
    Pages: 1772-1790

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    Handle: RePEc:eee:jmvana:v:101:y:2010:i:8:p:1772-1790
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    1. Joe, Harry, 1993. "Multivariate dependence measures and data analysis," Computational Statistics & Data Analysis, Elsevier, vol. 16(3), pages 279-297, September.
    2. Joe, Harry, 1990. "Multivariate concordance," Journal of Multivariate Analysis, Elsevier, vol. 35(1), pages 12-30, October.
    3. Fang, Kai-Tai & Fang, Bi-Qi, 1988. "Some families of mutivariate symmetric distributions related to exponential distribution," Journal of Multivariate Analysis, Elsevier, vol. 24(1), pages 109-122, January.
    4. Hofert, Marius, 2008. "Sampling Archimedean copulas," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5163-5174, August.
    5. Gupta, Rameshwar D. & Richards, Donald St. P., 1992. "Multivariate Liouville distributions, III," Journal of Multivariate Analysis, Elsevier, vol. 43(1), pages 29-57, October.
    6. Gupta, Rameshwar D. & Richards, Donald St.P., 1987. "Multivariate Liouville distributions," Journal of Multivariate Analysis, Elsevier, vol. 23(2), pages 233-256, December.
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