# Poisson-Kingman partitions

@article{Pitman2003PoissonKingmanP, title={Poisson-Kingman partitions}, author={Jim Pitman}, journal={arXiv: Probability}, year={2003}, pages={1-34} }

This paper presents some general formulas for random partitions of a finite set derived by Kingman's model of random sampling from an interval partition generated by subintervals whose lengths are the points of a Poisson point process. These lengths can be also interpreted as the jumps of a subordinator, that is an increasing process with stationary independent increments. Examples include the two-parameter family of Poisson-Dirichlet models derived from the Poisson process of jumps of a stable…

## 189 Citations

PR ] 2 4 O ct 2 00 2 Poisson-Kingman Partitions ∗

- Mathematics
- 2003

This paper presents some general formulas for random partitions of a finite set derived by Kingman’s model of random sampling from an interval partition generated by subintervals whose lengths are…

Regeneration in random combinatorial structures

- Mathematics
- 2009

Kingman’s theory of partition structures relates, via a natural
sampling procedure, finite partitions to hypothetical infinite populations.
Explicit formulas for distributions of such partitions…

DIRICHLET-KINGMAN PARTITION REVISITED

- Mathematics
- 2007

We reconsider the Dirichlet model for the random division of an interval. This model is parameterized by the number n > 1 of fragments, together with a set of positive parameters ( 1,..., n). Its…

Poisson Process Partition Calculus with applications to Exchangeable models and Bayesian Nonparametrics

- Mathematics
- 2002

This article discusses the usage of a partiton based Fubini calculus for Poisson processes. The approach is an amplification of Bayesian techniques developed in Lo and Weng for gamma/Dirichlet…

Characterizations of exchangeable partitions and random discrete distributions by deletion properties

- Mathematics
- 2009

We prove a long-standing conjecture which characterises the Ewens-Pitman two- parameter family of exchangeable random partitions, plus a short list of limit and exceptional cases, by the following…

Regenerative composition structures

- Mathematics
- 2003

A new class of random composition structures (the ordered analog of Kingman’s partition structures) is defined by a regenerative description of component sizes. Each regenerative composition…

Conditional formulae for Gibbs-type exchangeable random partitions

- Mathematics
- 2013

Gibbs-type random probability measures and the exchangeable random partitions they induce represent an important framework both from a theoretical and applied point of view. In the present paper,…

Exchangeable random partitions from max-infinitely-divisible distributions

- MathematicsStatistics & Probability Letters
- 2019

Asymptotics for the number of blocks in a conditional Ewens-Pitman sampling model

- Mathematics
- 2014

The study of random partitions has been an active research area in probability over the last twenty years. A quantity that has attracted a lot of attention is the number of blocks in the random…

On the stick-breaking representation of σ-stable Poisson-Kingman models

- Mathematics
- 2014

Abstract: In this paper we investigate the stick-breaking representation for the class of σ-stable Poisson-Kingman models, also known as Gibbs-type random probability measures. This class includes as…

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