Ordered and unordered random partitions of an integer and the GEM distribution
The authors show that the joint distribution of ordered (or unordered) frequencies of a sample from random proportions is the Donnelly-Tavaré-Griffiths formula (or the Ewens sampling formula) if and only if the size-biased permutation of the random proportions has the GEM distribution. Obtained results are related to those of \textit{J. F. C. Kingman} [Theor. Popul. Biol. 11, 274-283 (1977; Zbl 0421.92011)] and \textit{P. Donnelly} and \textit{P. Joyce} [Adv. Appl. Probab. 23, No. 2, 229-258 (1991; Zbl 0724.60040)].
scientific article; zbMATH DE number 844734