Matrix Variate Distributions

Zusatztext "This book is about probability distributions for random matrices." Biometrics! Vol. 56! No. 3! September 2000 "I am sure that the book will be welcomed by specialists! because of its systematic and thorough coverage of the different distributions." Biometrics! Vol. 56! No. 3! September 2000Promo Copy Informationen zum Autor A K Gupta, D K Nagar Klappentext 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. Zusammenfassung 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 distribution Wishart distribution Matrix variate t-distribution Matrix variate beta distribution F-distribution Matrix variate Dirichlet distribution Matrix quadratic forms With its inclusion of new results, Matrix Variate Distributions promises to stimulate further research and help advance the field of multivariate statistical analysis. Inhaltsverzeichnis 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 Distribu...

"This book is about probability distributions for random matrices." Biometrics, Vol. 56, No. 3, September 2000 "I am sure that the book will be welcomed by specialists, because of its systematic and thorough coverage of the different distributions." Biometrics, Vol. 56, No. 3, September 2000Promo Copy

Autorentext
A K Gupta, D K Nagar

Klappentext
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.

Zusammenfassung
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 distribution
Wishart distribution
Matrix variate t-distribution
Matrix variate beta distribution
F-distribution
Matrix variate Dirichlet distribution
Matrix quadratic forms
With its inclusion of new results, Matrix Variate Distributions promises to stimulate further research and help advance the field of multivariate statistical analysis.

Inhalt
PRELIMINARIES Matrix Algebra Jacobians of Transformations Integration Zonal Polynomials Hypergeometric Functions of Matrix Argument LaGuerre Polynomials Generalized Hermite Polynomials Notion of Random Matrix Problems MATRIX VARIATE NORMAL DISTRIBUTION Density Function Properties Singular Matrix Variate Normal distribution Symmetic Matrix Variate Normal Distribution Restricted Matrix Variate Normal Distribution Matrix Variate Q-Generalized Normal Distribution WISHART DISTRIBUTION Introduction Density Function Properties Inverted Wishart Distribution Noncentral Wishart Distribution Matrix Variate Gamma Distribution Approximations MATRIX VARIATE t-DISTRIBUTION Density Function Properties Inverted Matrix Variate t-Distribution Disguised Matrix Variate t-Distribution Restricted Matrix Variate t-Distribution Noncentral Matrix Variate t-Distribution Distribution of Quadratic Forms MATRIX VARIATE BETA DISTRIBUTIONS Density Functions Properties Related Distributions Noncentral Matrix Variate Beta Distribution MATRIX VARIATE DIRICHLET DISTRIBUTIONS Density Functions Properties Related Distributions Noncentral Matrix Variate Dirichlet Distributions DISTRIBUTION OF MATRIX QUADRATIC FORMS Density Function Properties Functions of Quadratic Forms Series Representation of the Density Noncentral Density Function Expected Values Wishartness and Independence of Quadratic Forms of the Type XAX' Wishartness and Independence of Quadratic Forms of the Type XAX'+1/2(LX'+XL')+C Wishartness and Independence of Quadratic Forms of the Type XAX'+L1X'+XL'2+C MISCELLANEOUS DISTRIBUTIONS Uniform Distribution on Stiefel Manifold Von Mises-Fisher Distribution Bingham Matrix Distribution Generalized Bingham-Von Mises Matrix Distribution Manifold Normal Distribution Matrix Angular Central Gaussian Distribution Bimatix Wishart Distribution Beta-Wishart Distribution Confluent Hypergeometric Function Kind 1 Distribution Confluent Hypergeometric Function Kind 2 Distribution Hypergeometric Function Distributions Generalized Hypergeometric Function Distributions Complex Matrix Variate Distributions GENERAL FAMILIES OF MATRIX VARIATE DISTRIBUTIONS Matrix Variate Liouville Distributions Matrix Variate Spherical Distributions Matrix Variate Elliptically Contoured Distributions Orthogonally Invariant and Residua…

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