Une caractérisation du type de la loi de Cauchy-conforme sur \({\mathbb{R}}^ n\). (A characterization of the type of the conformal Cauchy law on \({\mathbb{R}}^ n)\)
type: Item
instance of: scholarly article
title: Une caractérisation du type de la loi de Cauchy-conforme sur \({\mathbb{R}}^ n\). (A characterization of the type of the conformal Cauchy law on \({\mathbb{R}}^ n)\)
zbMATH Open document ID: 0662.62008
DOI: 10.1007/BF01848135
author: Jean-Louis Dunau
author: Henri Sénateur
publication date: 1988-01-01T00:00:00Z
review text: Let \(\mu\) be a measure defined on \(R^ n\) and consider the set of the images of \(\mu\) under similarities and translations of \(R^ n\). The authors term this set as the type of \(\mu\) and show that the conformal Cauchy distribution defined by the density \[ f(x)=c/(1+\| x\|^ 2)^ n,\quad x\in R^ n, \] is characterized by the invariance of the type of a non-atomic measure \(\mu\) on \(R^ n\) under inversions of \(R^ n\).
Mathematics Subject Classification ID: 62E10
zbMATH DE Number: 4082704
zbMATH Keywords: type of probability measures
zbMATH Keywords: characterization
zbMATH Keywords: transformations
zbMATH Keywords: similarities
zbMATH Keywords: translations
zbMATH Keywords: conformal Cauchy distribution
zbMATH Keywords: invariance
zbMATH Keywords: non-atomic measure
reviewed by: Evdokia Xekalaki
MaRDI profile type: Publication
cites work: Q5578241
cites work: An elementary proof of the Knight-Meyer characterization of the Cauchy distribution
cites work: Q4722906
cites work: A Characterization of the Cauchy Type
cites work: Une caract�risation de la loi de Cauchy
cites work: Q1088271
cites work: Q3969137
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
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description: scientific article; zbMATH DE number 4082704