Random discrete distributions invariant under size-biased permutation
- 1 June 1996
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 28 (2) , 525-539
- https://doi.org/10.2307/1428070
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
This publication has 17 references indexed in Scilit:
- Random Discrete Distributions Derived from Self-Similar Random SetsElectronic Journal of Probability, 1996
- Exchangeable and partially exchangeable random partitionsProbability Theory and Related Fields, 1995
- Continuity and weak convergence of ranked and size-biased permutations on the infinite simplexStochastic Processes and their Applications, 1989
- Size-biased filtering of Poisson–Dirichlet samples with an application to partition structures in geneticsJournal of Applied Probability, 1986
- On a Constant Arising in the Asymptotic Theory of Symmetric Groups, and on Poisson–Dirichlet MeasuresTheory of Probability and Its Applications, 1982
- The Representation of Partition StructuresJournal of the London Mathematical Society, 1978
- Stochastic Abundance ModelsPublished by Springer Nature ,1978
- The stationary distribution of the infinitely-many neutral alleles diffusion modelJournal of Applied Probability, 1976
- Concepts of Independence for Proportions with a Generalization of the Dirichlet DistributionJournal of the American Statistical Association, 1969
- Asymptotic Behavior of Bayes' EstimatesThe Annals of Mathematical Statistics, 1964