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Exact simulation of two-parameter Poisson-Dirichlet random variables

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  • Dassios, Angelos
  • Zhang, Junyi

Abstract

Consider a random vector (V1, . . . , Vn) where {Vk}k=1,...,n are the first n components of a two-parameter Poisson-Dirichlet distribution P D(α, θ). 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 θ/α 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.

Suggested Citation

  • Dassios, Angelos & Zhang, Junyi, 2021. "Exact simulation of two-parameter Poisson-Dirichlet random variables," LSE Research Online Documents on Economics 107937, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:107937
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    File URL: http://eprints.lse.ac.uk/107937/
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    References listed on IDEAS

    as
    1. Perman, Mihael, 1993. "Order statistics for jumps of normalised subordinators," Stochastic Processes and their Applications, Elsevier, vol. 46(2), pages 267-281, June.
    2. Sergey Sosnovskiy, 2015. "On financial applications of the two-parameter Poisson-Dirichlet distribution," Papers 1501.01954, arXiv.org, revised Jul 2015.
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    Cited by:

    1. Zhang, Junyi & Dassios, Angelos, 2023. "Truncated two-parameter Poisson-Dirichlet approximation for Pitman-Yor process hierarchical models," LSE Research Online Documents on Economics 120294, London School of Economics and Political Science, LSE Library.

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    More about this item

    Keywords

    two-parameter Poisson-Dirichlet distribution; exact simulation; subordinator;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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