The Annals of Probability

Distributional Results for Random Functionals of a Dirichlet Process

Robert C. Hannum, Myles Hollander, and Naftali A. Langberg

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We obtain an expression for the distribution function of the random variable $\int ZdP$ where $P$ is a random distribution function chosen by Ferguson's (1973) Dirichlet process on $(R, B)$ ($R$ is the real line and $B$ is the $\sigma$-field of Borel sets) with parameter $\alpha$, and $Z$ is a real-valued measurable function defined on $(R, B)$ satisfying $\int |Z| d\alpha < \infty$. As a consequence, we show that when $\alpha$ is symmetric about 0 and $Z$ is an odd function, then the distribution of $\int ZdP$ is symmetric about 0. Our main result is also used to obtain a new result for convergence in distribution of Dirichlet-based random functionals.

Article information

Ann. Probab., Volume 9, Number 4 (1981), 665-670.

First available in Project Euclid: 19 April 2007

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Zentralblatt MATH identifier


Primary: 60K99: None of the above, but in this section
Secondary: 60E05: Distributions: general theory

Dirichlet process distribution of random functionals


Hannum, Robert C.; Hollander, Myles; Langberg, Naftali A. Distributional Results for Random Functionals of a Dirichlet Process. Ann. Probab. 9 (1981), no. 4, 665--670. doi:10.1214/aop/1176994373.

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