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An Integral Characterization of the Dirichlet Process

  • Günter LastEmail author
Article
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Abstract

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.

Keywords

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

Mathematics Subject Classification (2010)

60G55 60G57 

Notes

Acknowledgements

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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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of StochasticsKarlsruhe Institute of TechnologyKarlsruheGermany

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