Regularity property of the functional equation of the Dirichlet distribution
type: Item
instance of: scholarly article
title: Regularity property of the functional equation of the Dirichlet distribution
zbMATH Open document ID: 0914.39029
published in: Aequationes Mathematicae
publication date: 1999-06-09T00:00:00Z
review text: The author deals with the functional equation \[ f_0 ( y_1, \dots, y_{n-1}) \prod^n_{j=1} g_j ( z_{i,j} , \dots, z_{k-1, j }) = g_0 ( x_1, \dots, x_{k-1}) \prod_{i=1}^k f_i ( w_{i,1}, \dots, w_{i, n-1}) . \tag{1} \] After the results obtained by \textit{D. Geiger} and \textit{D. Heckerman} [Ann. Stat. 25, No. 3, 1344-1369 (1997; Zbl 0885.62009)], characterizing the Dirichlet distribution, D. Geiger set the following problem: If the unknown functions in (1) are density functions, does it follow that they are positive everywhere and \( C^{\infty} \)? In this paper an elegant affirmative answer to this question is given.
reviewed by: Claudi Alsina
Mathematics Subject Classification ID: 39B22
Mathematics Subject Classification ID: 28C15
Mathematics Subject Classification ID: 60E05
zbMATH DE Number: 1220995
zbMATH Keywords: Dirichlet distribution
zbMATH Keywords: regularity property
zbMATH Keywords: functional equation
author: Antal jun. Járai
MaRDI profile type: Publication
full work available at URL: s000100050042
OpenAlex ID: W2001597719
DOI: 10.1007/S000100050042
description: scientific article; zbMATH DE number 1220995