An everywhere convergent series representation of the distribution of Hotelling's generalized \(T^ 2_ 0\) (Q1094041)
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scientific article; zbMATH DE number 4024537
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An everywhere convergent series representation of the distribution of Hotelling's generalized \(T^ 2_ 0\) |
scientific article; zbMATH DE number 4024537 |
Statements
An everywhere convergent series representation of the distribution of Hotelling's generalized \(T^ 2_ 0\) (English)
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1987
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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.
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null distribution
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explicit formulae
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non-central distributions
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Wishart distributions
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exact distribution
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invariant polynomials
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everywhere convergent series
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Hotelling generalized T-square distribution
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