An elementary proof of the Knight-Meyer characterization of the Cauchy distribution
type: Item
instance of: scholarly article
title: An elementary proof of the Knight-Meyer characterization of the Cauchy distribution
zbMATH Open document ID: 0655.62007
DOI: 10.1016/0047-259X(87)90076-5
author: Jean-Louis Dunau
author: Henri Sénateur
published in: Journal of Multivariate Analysis
publication date: 1987-01-01T00:00:00Z
review text: This paper propounds a short proof of a result previously proved by \textit{F. Knight} and \textit{P. A. Meyer} [Z. Wahrscheinlichkeitstheorie verw. Gebiete 34, 129-134 (1976; Zbl 0353.60020)]. Let X be a random variable in \({\mathbb{R}}^ n\) with the following property: for any matrix \(\left( \begin{matrix} a\quad b\\ c\quad d\end{matrix} \right)\) in \(GL(n+1)\) (where a is an (n,n) matrix) there exist \(\alpha\) in GL(n) and \(\beta\) in \({\mathbb{R}}^ n\) so that \((aX+b)/(cX+d)\) and \((\alpha X+\beta)\) have the same distribution. Then X is necessarily Cauchy distributed.
Mathematics Subject Classification ID: 62E10
Mathematics Subject Classification ID: 60E05
zbMATH DE Number: 4070019
zbMATH Keywords: Cauchy distribution
zbMATH Keywords: characterization
zbMATH Keywords: type
zbMATH Keywords: projective space
zbMATH Keywords: GL(n)
MaRDI profile type: Publication
cites work: Q5537437
cites work: A Characterization of the Cauchy Type
cites work: Une caract�risation de la loi de Cauchy
full work available at URL: 0047-259x(87)90076-5
OpenAlex ID: W2080528280
description: scientific article; zbMATH DE number 4070019