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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

         Jim Pitman,  Marc Yor (1997)
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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

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