Probability Theory and Related Fields

, Volume 102, Issue 2, pp 145–158

Exchangeable and partially exchangeable random partitions

  • Jim Pitman

DOI: 10.1007/BF01213386

Cite this article as:
Pitman, J. Probab. Th. Rel. Fields (1995) 102: 145. doi:10.1007/BF01213386


Call a random partition of the positive integerspartially exchangeable if for each finite sequence of positive integersn1,...,nk, the probability that the partition breaks the firstn1+...+nk integers intok particular classes, of sizesn1,...,nk in order of their first elements, has the same valuep(n1,...,nk) for every possible choice of classes subject to the sizes constraint. A random partition is exchangeable iff it is partially exchangeable for a symmetric functionp(n1,...nk). A representation is given for partially exchangeable random partitions which provides a useful variation of Kingman's representation in the exchangeable case. Results are illustrated by the two-parameter generalization of Ewens' partition structure.

Mathematics Subject Classification

60G09 60C05 60J50 

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Jim Pitman
    • 1
  1. 1.Department of StatisticsU.C. BerkeleyUSA

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