## The Annals of Statistics

### 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 $\mu^\ast$.

#### Article information

Source
Ann. Statist. Volume 1, Number 2 (1973), 353-355.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aos/1176342372

Digital Object Identifier
doi:10.1214/aos/1176342372

Mathematical Reviews number (MathSciNet)
MR362614

Zentralblatt MATH identifier
0276.62010

JSTOR
links.jstor.org

#### Citation

Blackwell, David; MacQueen, James B. Ferguson Distributions Via Polya Urn Schemes. Ann. Statist. 1 (1973), no. 2, 353--355. doi:10.1214/aos/1176342372. http://projecteuclid.org/euclid.aos/1176342372.