Extendibility of Marshall–Olkin distributions and inverse Pascal triangles

Abstract

Necessary and sufficient conditions are derived on the parameters of a $d$-dimensional random vector with Marshall–Olkin distribution to be extendible to an infinite exchangeable sequence. Interpreted differently, this result allows to decide if the respective multivariate exponential distribution can be constructed by means of a model with conditionally independent and identically distributed components. The proof makes use of the solution of the truncated Hausdorff moment problem and a reparameterization of the Marshall–Olkin distribution.