Matrix Variate Distributions

Abstract

The following sections are included:IntroductionSquare Random MatricesRectangular Random MatricesNormal Matrix VariatePropertiesDerived matrix distributionsFrom the Normal to the Gamma Family of DistributionsThe Wishart DistributionIts entries distributionCharacteristic functionAdditivityThe diagonal submatrices of a Wishart matrixDistributions of some ratiosBartlett decompositionDeterminant distributionLatent roots of a Wishart matrixThe Generalized VarianceExpression of the generalized varianceExpression of the density of the sample generalized varianceEstimation of |Σ|Numerical illustrationThe Matrix Variate Gamma DistributionThe Central Matrix Variate Beta DistributionsEntries distributionsDeterminant distributionLatent roots distributionsDecomposition of a beta matrix variateWilks’s distributionsConclusionBibliography

Topics & Concepts