Radial and directional parts of a random vector
type: Item
instance of: scholarly article
title: Radial and directional parts of a random vector
zbMATH Open document ID: 0633.62046
DOI: 10.1016/0167-7152(88)90112-5
author: Robert I. Jennrich
author: Sidney C. Port
published in: Statistics \& Probability Letters
publication date: 1988-01-01T00:00:00Z
review text: Let X be a random vector on \({\mathbb{R}}^ d\) and let \(R=| X|\) and for \(R\neq 0\) let \(W=X/R\). Necessary and sufficient conditions are given for R and W to be independent. If X has a non-singular normal distribution we show that the following three conditions are equivalent. (i) the components of X are independent and identically distributed with 0 means and positive variances. (ii) W is uniformly distributed on the unit sphere. (iii) R and W are independent.
Mathematics Subject Classification ID: 62H05
zbMATH DE Number: 4030729
zbMATH Keywords: isotropic distribution
zbMATH Keywords: spherical distribution
zbMATH Keywords: characterization
zbMATH Keywords: Necessary and sufficient conditions
zbMATH Keywords: non-singular normal distribution
zbMATH Keywords: uniformly distributed
zbMATH Keywords: unit sphere
zbMATH Keywords: independent
MaRDI profile type: Publication
full work available at URL: 0167-7152(88)90112-5
OpenAlex ID: W2016861534
cites work: A Characterization of the Gamma Distribution
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description: scientific article; zbMATH DE number 4030729