A simple procedure calculating the generalized Stieltjes transform of the mean of a Dirichlet process
type: Item
instance of: scholarly article
title: A simple procedure calculating the generalized Stieltjes transform of the mean of a Dirichlet process
zbMATH Open document ID: 0916.60046
DOI: 10.1016/S0167-7152(98)00034-0
author: Alessandra Guglielmi
published in: Statistics \& Probability Letters
publication date: 1999-07-12T00:00:00Z
review text: Let \(P_\alpha\) denote a Dirichlet process with parameter \(\alpha\) on the real line; i.e., \(P_\alpha\) is a random measure on \(\mathbb{R}\) such that, for any partition \(A_1,\dots, A_n\) of \(\mathbb{R}\), the vector \(P_\alpha(A_1),\dots, P_\alpha(A_n)\) has a Dirichlet distribution with parameters \(\alpha(A_1),\dots,\alpha(A_n)\). The distribution of the mean \(\Gamma_\alpha=\int x P_\alpha(dx)\) of \(P_\alpha\) was obtained by \textit{D. M. Cifarelli} and \textit{E. Regazzini} [Ann. Stat. 18, No. 1, 429-442 (1990; Zbl 0706.62012)] through calculating the generalized Stieltjes transform of \(\Gamma_\alpha\). The short note under review now suggests a simplified calculation based on an integral equation for the Laplace transform of \(\Gamma_\alpha\).
Mathematics Subject Classification ID: 60G57
Mathematics Subject Classification ID: 60E10
zbMATH DE Number: 1202803
zbMATH Keywords: Dirichlet process
zbMATH Keywords: random measure
zbMATH Keywords: generalized Stieltjes transform
reviewed by: Alexander Schied
MaRDI profile type: Publication
cites work: Distribution functions of means of a Dirichlet process
cites work: Q5849166
cites work: Q4776689
cites work: Q4839399
full work available at URL: s0167-7152(98)00034-0
OpenAlex ID: W2058157449
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description: scientific article; zbMATH DE number 1202803