Matrix Variate Distributions

Pham-Gia Thu

Chapter 12 in The Multivariate Normal Distribution:Theory and Applications, 2021, pp 377-398 from World Scientific Publishing Co. Pte. Ltd.

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

Keywords: Univariate Normal; Multivariate; Random Variable; Random Vector; Random Matrix; Applications: Education; Psychology; Quality Control; Pattern Recognition (search for similar items in EconPapers)
JEL-codes: C01 C1 C15 C4 C46 (search for similar items in EconPapers)
Date: 2021
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