The Poisson-Dirichlet distribution and the scale-invariant Poisson process (1999)
| Venue: | COMBIN. PROBAB. COMPUT |
| Citations: | 4 - 0 self |
BibTeX
@ARTICLE{Arratia99thepoisson-dirichlet,
author = {Richard Arratia and A. D. Barbour and Simon Tavaré},
title = {The Poisson-Dirichlet distribution and the scale-invariant Poisson process},
journal = {COMBIN. PROBAB. COMPUT},
year = {1999},
volume = {8},
pages = {407--416}
}
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Abstract
We show that the Poisson–Dirichlet distribution is the distribution of points in a scaleinvariant 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 � 1. Restricting both processes to (0,β] for 0 <β � 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.
