A PÓLYA URN MODEL WITH A CONTINUUM OF COLORS

HAJIME YAMATO

Department of Mathematics, Faculty of Science, Kagoshima University, 1-21-35 Kourimoto, Kagoshima 890, Japan

(Received October 7, 1991; revised September 14, 1992)

Abstract. For a Pólya urn model with a continuum of colors introduced by Blackwell and MacQueen ((1973), Ann. Statist., 2, 1152–1174), we show the joint distribution of colors after n draws from which several properties of the urn model are derived. The similar results hold for the case where the initial distribution of colors is invariant under a finite group of transformations.

Key words and phrases: Dirichlet process, Dirichlet invariant process, Stirling numbers of the first kind.