Ferguson Distributions Via Polya Urn Schemes

Abstract

The Polya urn scheme is extended by allowing a continuum of colors. For the extended scheme, the distribution of colors after $n$ draws is shown to converge as $n \\rightarrow \\infty$ to a limiting discrete distribution $\\mu^\\ast$. The distribution of $\\mu^\\ast$ is shown to be one introduced by Ferguson and, given $\\mu^\\ast$, the colors drawn from the urn are shown to be independent with distribution $\\mu^\\ast$.