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 $\alpha$-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 $\mathrm{PD}(\alpha ,0),\alpha \in (0,1)$ and $\mathrm{PD}(0,\theta ),\theta >0$.

9 pages, minor revision

References in corpus (1)

• Extreme-value copulas associated with the expected scaled maximum of independent random variables