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Distributions of Functionals of the two Parameter Poisson-Dirichlet Process

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  • Lancelot F. James
  • Antonio Lijoi
  • Igor Prünster

Abstract

The present paper provides exact expressions for the probability distribution of linear functionals of the two–parameter Poisson–Dirichlet process. Distributional results that follow from the application of an inversion formula for a (generalized) Cauchy–Stieltjes transform are achieved. Moreover, several interesting integral identities are obtained by exploiting a correspondence between the mean functional of a Poisson–Dirichlet process and the mean functional of a suitable Dirichlet process. Finally, some distributional characterizations in terms of mixture representations are illustrated. Our formulae are relevant to occupation time phenomena connected with Brownian motion and more general Bessel processes, as well as to models arising in Bayesian nonparametric statistics.

Suggested Citation

  • Lancelot F. James & Antonio Lijoi & Igor Prünster, 2006. "Distributions of Functionals of the two Parameter Poisson-Dirichlet Process," ICER Working Papers - Applied Mathematics Series 29-2006, ICER - International Centre for Economic Research.
    • Handle: RePEc:icr:wpmath:29-2006
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    References listed on IDEAS

    as
    1. Nils Hjort & Andrea Ongaro, 2005. "Exact Inference for Random Dirichlet Means," Statistical Inference for Stochastic Processes, Springer, vol. 8(3), pages 227-254, December.
    2. Ishwaran H. & James L. F, 2001. "Gibbs Sampling Methods for Stick Breaking Priors," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 161-173, March.
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