An everywhere convergent series representation of the distribution of Hotelling's generalized \(T^ 2_ 0\)
type: Item
instance of: scholarly article
title: An everywhere convergent series representation of the distribution of Hotelling's generalized \(T^ 2_ 0\)
zbMATH Open document ID: 0629.62055
DOI: 10.1016/0047-259X(87)90003-0
published in: Journal of Multivariate Analysis
publication date: 1987-01-01T00:00:00Z
review text: Hotelling's verallgemeinerte \(T^ 2_ 0\)-Statistik ist definiert als \(n_ 2\cdot Spur(S_ 1S_ 2^{-1})\), wobei \(S_ 1\) und \(S_ 2\) unabhängige (m\(\times m)\) Wishartmatrizen mit \(n_ 1\) resp. \(n_ 2\) Freiheitsgraden sind. Die Nullverteilung von \(T=T^ 2_ 0/n_ 2\) wurde für \(m=2\) bereits von Hotelling als Reihe hergeleitet. Dieses Resultat erfuhr viele Verallgemeinerungen und wird hier als eine überall konvergente Reihe dargestellt.
Mathematics Subject Classification ID: 62H10
Mathematics Subject Classification ID: 40A30
Mathematics Subject Classification ID: 62E15
zbMATH DE Number: 4024537
zbMATH Keywords: null distribution
zbMATH Keywords: explicit formulae
zbMATH Keywords: non-central distributions
zbMATH Keywords: Wishart distributions
zbMATH Keywords: exact distribution
zbMATH Keywords: invariant polynomials
zbMATH Keywords: everywhere convergent series
zbMATH Keywords: Hotelling generalized T-square distribution
author: Peter C. B. Phillips
reviewed by: Peter Nueesch
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4024537