The Poisson–Dirichlet Distribution and the Scale-Invariant Poisson Process
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The Poisson-Dirichlet Distribution And The Scale-Invariant Poisson Process
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 6 1. Restricting both processes to (0, β] for 0 < β 6 1, we give an explicit formula for the ...
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ژورنال
عنوان ژورنال: Combinatorics, Probability and Computing
سال: 1999
ISSN: 0963-5483,1469-2163
DOI: 10.1017/s0963548399003910