Displaying similar documents to “A characterization of matrix variate normal distribution.”

A generalization of Wishart density for the case when the inverse of the covariance matrix is a band matrix

Kryštof Eben (1994)

Mathematica Bohemica

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In a multivariate normal distribution, let the inverse of the covariance matrix be a band matrix. The distribution of the sufficient statistic for the covariance matrix is derived for this case. It is a generalization of the Wishart distribution. The distribution may be used for unbiased density estimation and construction of classification rules.

Densities of determinant ratios, their moments and some simultaneous confidence intervals in the multivariate Gauss-Markoff model

Wiktor Oktaba (1995)

Applications of Mathematics

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The following three results for the general multivariate Gauss-Markoff model with a singular covariance matrix are given or indicated. 1 ∘ determinant ratios as products of independent chi-square distributions, 2 ∘ moments for the determinants and 3 ∘ the method of obtaining approximate densities of the determinants.

The Lukacs-Olkin-Rubin theorem without invariance of the "quotient"

Konstancja Bobecka, Jacek Wesołowski (2002)

Studia Mathematica

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The Lukacs theorem is one of the most brilliant results in the area of characterizations of probability distributions. First, because it gives a deep insight into the nature of independence properties of the gamma distribution; second, because it uses beautiful and non-trivial mathematics. Originally it was proved for probability distributions concentrated on (0,∞). In 1962 Olkin and Rubin extended it to matrix variate distributions. Since that time it has been believed that the fundamental...