An Integral Characterization of the Dirichlet Process


We give a new integral characterization of the Dirichlet process on a general phase space. To do so, we first prove a characterization of the nonsymmetric Beta distribution via size-biased sampling. Two applications are a new characterization of the Dirichlet distribution and a marked version of a classical characterization of the Poisson–Dirichlet distribution via invariance and independence properties.

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I wish to thank Lorenzo Dello Schiavo for drawing my attention to the topic of the paper and the referee for making several helpful comments.

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Correspondence to Günter Last.

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Last, G. An Integral Characterization of the Dirichlet Process. J Theor Probab 33, 918–930 (2020).

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  • Dirichlet process
  • Dirichlet distribution
  • Beta distribution
  • Poisson process
  • Mecke equation
  • Poisson–Dirichlet distribution
  • Size-biased sampling

Mathematics Subject Classification (2010)

  • 60G55
  • 60G57