An Integral Characterization of the Dirichlet Process
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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 and independence properties.
KeywordsDirichlet process Dirichlet distribution Beta distribution Poisson process Mecke equation Poisson–Dirichlet distribution Size-biased sampling
Mathematics Subject Classification (2010)60G55 60G57
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.
- 1.Dello Schiavo, L., Lytvynov, E.W.: A Mecke-type characterization of the Dirichlet–Ferguson measure. (2017). arXiv:1706.07602
- 8.McCloskey, J.W.: A Model for the Distribution of Individuals by Species in an Environment. Unpublished Ph.D. Dissertation Thesis, Michigan State University (1965)Google Scholar
- 11.Pitman, J.: Some developments of the Blackwell–MacQueen urn scheme. In: Ferguson, T.S., Shapley, L.S., MacQueen, J.B. (eds.), Statistics, Probability and Game Theory. IMS Lecture Notes-Monograph Series, vol. 30, pp. 245–267 (1995)Google Scholar