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A multivariate version of Williamson’s theorem, ℓ1-symmetric survival functions, and generalized Archimedean copulas

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  • Ressel Paul

    (Kath. Universität Eichstätt-Ingolstadt,Eichstätt, Deutschland)

Abstract

Williamson’s integral representation of n-monotone functions on the half-line is generalized to several dimensions. This leads to a characterization of multivariate survival functions with multiply ℓ1- symmetry. We then introduce a new class of generalized Archimedean copulas, where in contrast to nested Archimedean copulas no extra compatibility conditions for their generators are required.

Suggested Citation

  • Ressel Paul, 2018. "A multivariate version of Williamson’s theorem, ℓ1-symmetric survival functions, and generalized Archimedean copulas," Dependence Modeling, De Gruyter, vol. 6(1), pages 356-368, December.
    • Handle: RePEc:vrs:demode:v:6:y:2018:i:1:p:356-368:n:20
    DOI: 10.1515/demo-2018-0020
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    References listed on IDEAS

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    1. Ressel, Paul, 2011. "Monotonicity properties of multivariate distribution and survival functions -- With an application to Lévy-frailty copulas," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 393-404, March.
    2. Ressel, Paul, 2012. "Functions operating on multivariate distribution and survival functions—With applications to classical mean-values and to copulas," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 55-67.
    3. Cossette, Hélène & Gadoury, Simon-Pierre & Marceau, Étienne & Mtalai, Itre, 2017. "Hierarchical Archimedean copulas through multivariate compound distributions," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 1-13.
    4. Ressel, Paul, 2013. "Homogeneous distributions—And a spectral representation of classical mean values and stable tail dependence functions," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 246-256.
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