An integral characterization of the Dirichlet process
classification
🧮 math.PR
keywords
characterizationdirichletdistributionintegralprocesssamplingsize-biasedapplications
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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 under size-biased sampling.
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