Some remarks on \({\mathcal U}(p;m,n)\) distributions
type: Item
instance of: scholarly article
title: Some remarks on \({\mathcal U}(p;m,n)\) distributions
zbMATH Open document ID: 0877.62050
DOI: 10.1016/S0167-7152(96)00011-9
author: Martin Bilodeau
published in: Statistics \& Probability Letters
publication date: 1997-11-24T00:00:00Z
review text: For independent \(p\)-dimensional random vectors \(X_i\), \(i=1,\dots,n\), each having standard normal distribution \(N(0,I)\), the distribution of the \(p\times p\) random matrix \(\sum_{i=1}^nX_iX_i'\) is called the Wishart distribution \(W_p(n)\). A random variable \(U\) has distribution \({\mathcal U}(p;m,n)\) if it is equal in distribution to \(|W_1|/|W_1+W_2|\) for two independent \(p\times p\) random matrices \(W_1, W_2\) having the distributions \(W_p(n)\) and \(W_p(m)\) with \(m+n>p\). In the paper under review simple proofs are given for several known properties of \({\mathcal U}(p;m,n)\) distributions.
Mathematics Subject Classification ID: 62H05
Mathematics Subject Classification ID: 60E05
zbMATH DE Number: 1031720
zbMATH Keywords: Wishart distribution
zbMATH Keywords: U(p
zbMATH Keywords: m,n) distribution
zbMATH Keywords: duality
reviewed by: Rimas Norvaiša
MaRDI profile type: Publication
cites work: Q3796553
cites work: Q5777633
cites work: Q3713374
cites work: Distribution of the `Generalised' Multiple Correlation Matrix in the Dual Case
cites work: The Non-Central Multivariate Beta Distribution
cites work: Q3219581
Wikidata QID: Q126563004
description: scientific article; zbMATH DE number 1031720