Exchangeable random partitions from max-infinitely-divisible distributions

Abstract

The hitting partitions are random partitions that arise from the investigation of so-called hitting scenarios of max-infinitely-divisible (max-i.d.) distributions. We study a class of max-i.d. laws with exchangeable hitting partitions obtained by size-biased sampling from the jumps of a Lévy subordinator. We obtain explicit formulae for the distributions of these partitions in the case of the multivariate α-logistic and another family of exchangeable max-i.d. distributions. Specifically, the hitting partitions for these two cases are shown to coincide with the well-known Poisson–Dirichlet partitions PD(α,0),α∈(0,1) and PD(0,θ),θ>0.