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Matrix Variate Distributions

In: THE MULTIVARIATE NORMAL DISTRIBUTION Theory and Applications

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  • PHAM-GIA THU

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

Suggested Citation

  • Pham-Gia Thu, 2021. "Matrix Variate Distributions," World Scientific Book Chapters, in: THE MULTIVARIATE NORMAL DISTRIBUTION Theory and Applications, chapter 12, pages 377-398, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789811235290_0012
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    More about this item

    Keywords

    Univariate Normal; Multivariate; Random Variable; Random Vector; Random Matrix; Applications: Education; Psychology; Quality Control; Pattern Recognition;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics

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