## The Annals of Statistics

### The Tails of Probabilities Chosen From A Dirichlet Prior

#### Abstract

Let $\alpha$ be a finite nonnull measure on $\mathbb{R}$, and let the random distribution function $F$ be distributed according to $\mathbb{D}_\alpha$, where $\mathbb{D}_\alpha$ is the Dirichlet process prior with parameter $\alpha$; see Ferguson (1973). This note points out that, almost surely, the tails of $F$ are much smaller than the tails of $\alpha$.

#### Article information

Source
Ann. Statist., Volume 10, Number 4 (1982), 1302-1305.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176345996

Digital Object Identifier
doi:10.1214/aos/1176345996

Mathematical Reviews number (MathSciNet)
MR673666

Zentralblatt MATH identifier
0515.62008

JSTOR