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Large deviations for Dirichlet processes and Poisson-Dirichlet distributions with two parameters

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Abstract

Large deviation principles are established for the two-parameter Poisson-Dirichlet distribution and two-parameter Dirichlet process when parameter $$\theta$$ approaches infinity. The motivation for these results is to understand the differences in terms of large deviations between the two-parameter models and their one-parameter counterparts. New insight is obtained about the role of the second parameter $$\alpha$$ through a comparison with the corresponding results for the one-parameter Poisson-Dirichlet distribution and Dirichlet process.

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The Relation Between the Number of Species and the Number of Individuals in a Random Sample of an Animal Population

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The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator

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Exchangeable and partially exchangeable random partitions

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Author and article information

Journal
22 November 2006
math/0611706
Custom metadata
60F10; 92D10
22 pages
math.PR