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

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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}.

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  1. Math.-Geogr. Fakultät, Kath. Univ. Eichstätt-Ingolstadt, 85071, Eichstätt, Germany

    Paul Ressel

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  1. Paul Ressel
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Correspondence to Paul Ressel.

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Ressel, P. Finite Exchangeability, Lévy-Frailty Copulas and Higher-Order Monotonic Sequences. J Theor Probab 26, 666–675 (2013). https://doi.org/10.1007/s10959-011-0389-9

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  • DOI: https://doi.org/10.1007/s10959-011-0389-9

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