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Finite Exchangeability, Lévy-Frailty Copulas and Higher-Order Monotonic Sequences

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  • Paul Ressel

    (Kath. Univ. Eichstätt-Ingolstadt)

Abstract

This paper deals with a surprising connection between exchangeable distributions on {0,1} n and the recently introduced Lévy-frailty copulas, the link being provided by a new class of multivariate distribution functions called linearly order symmetric. The characterisation theorem for Lévy-frailty copulas is given a new and short (non-combinatorial) proof, and a related result is shown for exchangeable Marshall–Olkin distributions. A common thread in all these considerations is higher-order monotonic functions on integer intervals of the form {0,1,…,n}.

Suggested Citation

  • Paul Ressel, 2013. "Finite Exchangeability, Lévy-Frailty Copulas and Higher-Order Monotonic Sequences," Journal of Theoretical Probability, Springer, vol. 26(3), pages 666-675, September.
    • Handle: RePEc:spr:jotpro:v:26:y:2013:i:3:d:10.1007_s10959-011-0389-9
    DOI: 10.1007/s10959-011-0389-9
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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. Mai, Jan-Frederik & Scherer, Matthias, 2009. "Lévy-frailty copulas," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1567-1585, August.
    3. Haijun Li, 2008. "Tail Dependence Comparison of Survival Marshall–Olkin Copulas," Methodology and Computing in Applied Probability, Springer, vol. 10(1), pages 39-54, March.
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    Cited by:

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