Matrix Variate Distributions

Presents most of the developments in continuous matrix variate distribution theory. This work investigates the range of matrix variate distributions, including: matrix variate normal distribution; Wishart distribution; Matrix variate t-distribution; Matrix variate beta distribution; F-distribution; and, Matrix variate Dirichlet distribution.

Useful in physics, economics, psychology, and other fields, random matrices play an important role in the study of multivariate statistical methods. Until now, however, most of the material on random matrices could only be found scattered in various statistical journals. Matrix Variate Distributions gathers and systematically presents most of the recent developments in continuous matrix variate distribution theory and includes new results.After a review of the essential background material, the authors investigate the range of matrix variate distributions, including:matrix variate normal distributionWishart distributionMatrix variate t-distributionMatrix variate beta distributionF-distributionMatrix variate Dirichlet distributionMatrix quadratic formsWith its inclusion of new results, Matrix Variate Distributions promises to stimulate further research and help advance the field of multivariate statistical analysis.

PRELIMINARIESMatrix AlgebraJacobians of TransformationsIntegrationZonal PolynomialsHypergeometric Functions of Matrix ArgumentLaGuerre PolynomialsGeneralized Hermite PolynomialsNotion of Random Matrix ProblemsMATRIX VARIATE NORMAL DISTRIBUTIONDensity FunctionPropertiesSingular Matrix Variate Normal distributionSymmetic Matrix Variate Normal DistributionRestricted Matrix Variate Normal DistributionMatrix Variate Q-Generalized Normal DistributionWISHART DISTRIBUTIONIntroductionDensity FunctionPropertiesInverted Wishart DistributionNoncentral Wishart DistributionMatrix Variate Gamma DistributionApproximationsMATRIX VARIATE t-DISTRIBUTIONDensity FunctionPropertiesInverted Matrix Variate t-DistributionDisguised Matrix Variate t-DistributionRestricted Matrix Variate t-DistributionNoncentral Matrix Variate t-DistributionDistribution of Quadratic FormsMATRIX VARIATE BETA DISTRIBUTIONSDensity FunctionsPropertiesRelated DistributionsNoncentral Matrix Variate Beta DistributionMATRIX VARIATE DIRICHLET DISTRIBUTIONSDensity FunctionsPropertiesRelated DistributionsNoncentral Matrix Variate Dirichlet DistributionsDISTRIBUTION OF MATRIX QUADRATIC FORMSDensity FunctionPropertiesFunctions of Quadratic FormsSeries Representation of the DensityNoncentral Density FunctionExpected ValuesWishartness and Independence of Quadratic Forms of the Type XAX'Wishartness and Independence of Quadratic Forms of the Type XAX'+1/2(LX'+XL')+CWishartness and Independence of Quadratic Forms of the Type XAX'+L1X'+XL'2+CMISCELLANEOUS DISTRIBUTIONSUniform Distribution on Stiefel ManifoldVon Mises-Fisher DistributionBingham Matrix DistributionGeneralized Bingham-Von Mises Matrix DistributionManifold Normal DistributionMatrix Angular Central Gaussian DistributionBimatix Wishart DistributionBeta-Wishart DistributionConfluent Hypergeometric Function Kind 1 DistributionConfluent Hypergeometric Function Kind 2 DistributionHypergeometric Function DistributionsGeneralized Hypergeometric Function DistributionsComplex Matrix Variate DistributionsGENERAL FAMILIES OF MATRIX VARIATE DISTRIBUTIONSMatrix Variate Liouville DistributionsMatrix Variate Spherical DistributionsMatrix Variate Elliptically Contoured DistributionsOrthogonally Invariant and Residual Independent Matrix DistributionsGLOSSARYREFERENCESSUBJECT INDEX Each chapter also includes an Introduction and Problems@