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August, 1981 Distributional Results for Random Functionals of a Dirichlet Process
Robert C. Hannum, Myles Hollander, Naftali A. Langberg
Ann. Probab. 9(4): 665-670 (August, 1981). DOI: 10.1214/aop/1176994373


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.


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Robert C. Hannum. Myles Hollander. Naftali A. Langberg. "Distributional Results for Random Functionals of a Dirichlet Process." Ann. Probab. 9 (4) 665 - 670, August, 1981.


Published: August, 1981
First available in Project Euclid: 19 April 2007

zbMATH: 0473.60019
MathSciNet: MR630318
Digital Object Identifier: 10.1214/aop/1176994373

Primary: 60K99
Secondary: 60E05

Keywords: Dirichlet process , distribution of random functionals

Rights: Copyright © 1981 Institute of Mathematical Statistics

Vol.9 • No. 4 • August, 1981
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