## The Annals of Statistics

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

### Distribution Functions of Means of a Dirichlet Process

Donato Michele Cifarelli and Eugenio Regazzini

#### 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**

links.jstor.org

**Subjects**

Primary: 62G99: None of the above, but in this section

Secondary: 62E15: Exact distribution theory 60K99: None of the above, but in this section 44A15: Special transforms (Legendre, Hilbert, etc.)

**Keywords**

Dirichlet probability distribution function Dirichlet process distribution of random functionals generalized Stieltjes transform

#### Citation

Cifarelli, Donato Michele; Regazzini, Eugenio. Distribution Functions of Means of a Dirichlet Process. Ann. Statist. 18 (1990), no. 1, 429--442. doi:10.1214/aos/1176347509. https://projecteuclid.org/euclid.aos/1176347509

#### Corrections

- See Correction: Donato Michele Cifarelli, Eugenio Regazzini. Correction: Distribution Functions of Means of a Dirichlet Process. Ann. Statist., Volume 22, Number 3 (1994), 1633--1634.Project Euclid: euclid.aos/1176325647