Matrix Variate Distributions

A K Gupta, D K Nagar

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 Residual Independent Matrix Distributions GLOSSARY REFERENCES SUBJECT INDEX Each chapter also includes an Introduction and Problems @