DOI

We describe the distribution of frequencies ordered by sample values in a random sample of size n from the two parameter GEM(a, ?) random discrete distribution on the positive integers. These frequencies are a (size-a)-biased random permutation of the sample frequencies in either ranked order, or in the order of appearance of values in the sampling process. This generalizes a well-known identity in distribution due to Donnelly and Tavaré [Adv. in Appl. Probab. 18 (1986) 1–19] for a = 0 to the case 0 = a < 1. This description extends to sampling from Gibbs(a) frequencies obtained by suitable conditioning of the GEM(a, ?) model, and yields a value-ordered version of the Chinese restaurant construction of GEM(a, ?) and Gibbs(a) frequencies in the more usual size-biased order of their appearance. The proofs are based on a general construction of a finite sample (X1, . . ., Xn) from any random frequencies in size-biased order from the associated exchangeable random partition 8 of N which they generate.

Original languageEnglish
Pages (from-to)1793-1820
Number of pages28
JournalAnnals of Applied Probability
Volume28
Issue number3
DOIs
StatePublished - 1 Jun 2018

    Research areas

  • Chinese restaurant construction, GEM distribution, Gibbs’ partitions, Random exchangeable partition, Size-biased order, Species sampling, PRIORS, ALLELES, REPRESENTATION, EXCHANGEABLE RANDOM PARTITIONS, DISTRIBUTIONS, Gibbs' partitions, random exchangeable partition, REVERSIBILITY, DIFFUSION, size-biased order, AGE

    Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

ID: 32734430