Distribution of random functional of a Dirichlet process on the unit disk (Q1181116)
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scientific article; zbMATH DE number 27778
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Distribution of random functional of a Dirichlet process on the unit disk |
scientific article; zbMATH DE number 27778 |
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Distribution of random functional of a Dirichlet process on the unit disk (English)
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27 June 1992
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Let \(U\) be a Dirichlet process with parameter \(\mu\) on the unit disk. It is shown that the vector \((X,Y)\) has a p.d.f. \((c/\pi)(1-x^ 2-y^ 2)^{c-1}\), \(0<x^ 2+y^ 2<1\), where \(X+iY=\int_ 0^{2\pi}\exp\{(2\pi i/c)\mu((0,\theta))\}dU(\theta)\) and \(c=\mu((0,\theta))\).
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characteristic function
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spherical distribution
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Dirichlet process
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