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

Kurzfassung/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}.