The distribution of frequencies of discrete order statistics and the donnelly-tavaré-griffiths formula

Abstract

A prior distribution is considered on the set of nonparametric discrete distributions whose support consists of infinitely many points. For the sample from a discrete distribution having this a prior distribution, we consider the frequency of discrete order statistics of the sample. We derive properties of a prior distribution such that the frequencies of discrete order statistics have the DTG(Donnelly-Tavaré-Griffiths) formula. Using these properties, we prove the proposition that only the GEM distribution gives rise to the DTG formula. This proposition is proved by Donnelly and Joyce [3] with asymptotic discussion. But out approach is different from them and use properties of a prior distribution which we derive.