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2021 Exact simulation of two-parameter Poisson-Dirichlet random variables
Angelos Dassios, Junyi Zhang
Electron. J. Probab. 26: 1-20 (2021). DOI: 10.1214/20-EJP573

Abstract

Consider a random vector $(V_{1}, \dots , V_{n})$ where $\{V_{k}\}_{k=1, \dots , n}$ are the first $n$ components of a two-parameter Poisson-Dirichlet distribution $PD(\alpha , \theta )$. In this paper, we derive a decomposition for the components of the random vector, and propose an exact simulation algorithm to sample from the random vector. Moreover, a special case arises when $\theta /\alpha $ is a positive integer, for which we present a very fast modified simulation algorithm using a compound geometric representation of the decomposition. Numerical examples are provided to illustrate the accuracy and effectiveness of our algorithms.

Citation

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Angelos Dassios. Junyi Zhang. "Exact simulation of two-parameter Poisson-Dirichlet random variables." Electron. J. Probab. 26 1 - 20, 2021. https://doi.org/10.1214/20-EJP573

Information

Received: 14 May 2020; Accepted: 17 December 2020; Published: 2021
First available in Project Euclid: 7 January 2021

Digital Object Identifier: 10.1214/20-EJP573

Subjects:
Primary: 60G57
Secondary: 60G51, 65C10

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Vol.26 • 2021
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