## The Annals of Statistics

### Distribution Functions of Means of a Dirichlet Process

#### Abstract

Let $\chi$ be a random probability measure chosen by a Dirichlet process on $(\mathbb{R}, \mathscr{B})$ with parameter $\alpha$ and such that $\int x\chi(dx)$ turns out to be a (finite) random variable. The main concern of this paper is the statement of a suitable expression for the distribution function of that random variable. Such an expression is deduced through an extension of a procedure based on the use of generalized Stieltjes transforms, originally proposed by the present authors in 1978.

#### Article information

Source
Ann. Statist., Volume 18, Number 1 (1990), 429-442.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176347509

Digital Object Identifier
doi:10.1214/aos/1176347509

Mathematical Reviews number (MathSciNet)
MR1041402

Zentralblatt MATH identifier
0706.62012

JSTOR