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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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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|Item Type:||Journal Article, refereed, original work|
|Communities & Collections:||07 Faculty of Science > Institute of Mathematics|
|Dewey Decimal Classification:||510 Mathematics|
|Deposited On:||07 Apr 2010 13:30|
|Last Modified:||27 Nov 2013 23:22|
|Publisher:||Cambridge University Press|
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