THE POISSON-DIRICHLET DISTRIBUTION AND ITS RELATIVES REVISITED
Lars K. Holst · 2001
The Poisson-Dirichlet distribution and its marginals are studied, in particular the largest component, that is Dickman's distribution. Size-biased sampling and the GEM distribution are considered. Ewens sampling formula and random permutations, generated by the Chinese restaurant process, are also investigated. The used methods are elementary and based on properties of the finite-dimensional Dirichlet distribution. Keywords: Chinese restaurant process; Dickman's function; Ewens sampling formula; GEM distribution; Hoppe's urn; random permutations; residual allocation models; size-biased sampling ams 1991 subject classification: primary 60g57 secondary 60c05, 60k99 Running title: The Poisson--Dirichlet distribution revisited 1