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November 2009 The two-parameter Poisson–Dirichlet point process
Kenji Handa
Bernoulli 15(4): 1082-1116 (November 2009). DOI: 10.3150/08-BEJ180


The two-parameter Poisson–Dirichlet distribution is a probability distribution on the totality of positive decreasing sequences with sum 1 and hence considered to govern masses of a random discrete distribution. A characterization of the associated point process (that is, the random point process obtained by regarding the masses as points in the positive real line) is given in terms of the correlation functions. Using this, we apply the theory of point processes to reveal the mathematical structure of the two-parameter Poisson–Dirichlet distribution. Also, developing the Laplace transform approach due to Pitman and Yor, we are able to extend several results previously known for the one-parameter case. The Markov–Krein identity for the generalized Dirichlet process is discussed from the point of view of functional analysis based on the two-parameter Poisson–Dirichlet distribution.


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Kenji Handa. "The two-parameter Poisson–Dirichlet point process." Bernoulli 15 (4) 1082 - 1116, November 2009.


Published: November 2009
First available in Project Euclid: 8 January 2010

zbMATH: 1255.60020
MathSciNet: MR2597584
Digital Object Identifier: 10.3150/08-BEJ180

Keywords: correlation function , Markov–Krein identity , point process , Poisson–Dirichlet distribution

Rights: Copyright © 2009 Bernoulli Society for Mathematical Statistics and Probability


Vol.15 • No. 4 • November 2009
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