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Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-22119

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.

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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.

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
DDC:510 Mathematics
Language:English
Date:1999
Deposited On:07 Apr 2010 13:30
Last Modified:27 Nov 2013 23:22
Publisher:Cambridge University Press
ISSN:0963-5483
Publisher DOI:10.1017/S0963548399003910
Citations:Web of Science®. Times Cited: 11
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Scopus®. Citation Count: 8

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