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Random discrete distributions invariant under size-biased permutation

Part of: Stochastic processes Distribution theory

Published online by Cambridge University Press:  01 July 2016

Jim Pitman
Jim Pitman*
Affiliation:
University of California at Berkeley
*
∗ Postal address: Department of Statistics, U.C. Berkeley, CA 94720, USA.
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Abstract

Invariance of a random discrete distribution under size-biased permutation is equivalent to a conjunction of symmetry conditions on its finite-dimensional distributions. This is applied to characterize residual allocation models with independent factors that are invariant under size-biased permutation. Apart from some exceptional cases and minor modifications, such models form a two-parameter family of generalized Dirichlet distributions.

Keywords

RESIDUAL ALLOCATION MODELEXCHANGEABLE RANDOM PARTITIONGENERALIZED DIRICHLET DISTRIBUTION

MSC classification

Primary: 62E10: Characterization and structure theory
Secondary: 60G09: Exchangeability
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 28 , Issue 2 , June 1996 , pp. 525 - 539
Copyright
Copyright © Applied Probability Trust 1996 

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Footnotes

Research supported by N.S.F. Grants MCS91–07531 and DMS-9404345.

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