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The Poisson-Dirichlet distribution and the scale-invariant Poisson process


Arratia, R; Barbour, A D; Tavaré, S (1999). The Poisson-Dirichlet distribution and the scale-invariant Poisson process. Combinatorics, Probability & Computing, 8(5):407-416.

Abstract

We show that the Poisson–Dirichlet distribution is the distribution of points in a scale-invariant Poisson process, conditioned on the event that the sum T of the locations of the points in (0,1] is 1. This extends to a similar result, rescaling the locations by T, and conditioning on the event that T[less-than-or-eq, slant]1. Restricting both processes to (0, [beta]] for 0<[beta][less-than-or-eq, slant]1, we give an explicit formula for the total variation distance between their distributions. Connections between various representations of the Poisson–Dirichlet process are discussed.

Abstract

We show that the Poisson–Dirichlet distribution is the distribution of points in a scale-invariant Poisson process, conditioned on the event that the sum T of the locations of the points in (0,1] is 1. This extends to a similar result, rescaling the locations by T, and conditioning on the event that T[less-than-or-eq, slant]1. Restricting both processes to (0, [beta]] for 0<[beta][less-than-or-eq, slant]1, we give an explicit formula for the total variation distance between their distributions. Connections between various representations of the Poisson–Dirichlet process are discussed.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > Theoretical Computer Science
Physical Sciences > Statistics and Probability
Physical Sciences > Computational Theory and Mathematics
Physical Sciences > Applied Mathematics
Language:English
Date:1999
Deposited On:07 Apr 2010 13:30
Last Modified:03 May 2024 01:38
Publisher:Cambridge University Press
ISSN:0963-5483
OA Status:Green
Publisher DOI:https://doi.org/10.1017/S0963548399003910