UZH-Logo

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.

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.

Citations

11 citations in Web of Science®
8 citations in Scopus®
Google Scholar™

Altmetrics

Downloads

23 downloads since deposited on 07 Apr 2010
8 downloads since 12 months
Detailed statistics

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:1999
Deposited On:07 Apr 2010 13:30
Last Modified:05 Apr 2016 13:26
Publisher:Cambridge University Press
ISSN:0963-5483
Publisher DOI:10.1017/S0963548399003910
Permanent URL: http://doi.org/10.5167/uzh-22119

Download

[img]
Preview
Filetype: PDF
Size: 1MB
View at publisher

TrendTerms

TrendTerms displays relevant terms of the abstract of this publication and related documents on a map. The terms and their relations were extracted from ZORA using word statistics. Their timelines are taken from ZORA as well. The bubble size of a term is proportional to the number of documents where the term occurs. Red, orange, yellow and green colors are used for terms that occur in the current document; red indicates high interlinkedness of a term with other terms, orange, yellow and green decreasing interlinkedness. Blue is used for terms that have a relation with the terms in this document, but occur in other documents.
You can navigate and zoom the map. Mouse-hovering a term displays its timeline, clicking it yields the associated documents.

Author Collaborations