【作者(必填)】A.K. Gupta, D.K. Nagar.

【文题(必填)】Matrix variate distributions

【年份(必填)】1999

【全文链接或数据库名称(选填)】http://www.amazon.com/Variate-Distributions-Monographs-Surveys-Mathematics/dp/1584880465

Summary: Publisher Summary 1 Gathers together recent developments in continuous matrix variate distribution theory, provides an analytical review of the material, and offers new results that will stimulate further research. Assumes familiarity with introductory multivariate statistical analysis and matrix algebra, and includes chapter problems and a glossary. For researchers and graduate students in multivariate statistical analysis and the investigation sciences. Gupta teaches mathematics and statistics at Bowling Green State University. Nagar teaches mathematics at the University of Antioquia, Colombia. Annotation c. Book News, Inc., Portland, OR (booknews.com)  (收起)
图书目录  Preliminaries p. 1
Introduction p. 1
Matrix Algebra p. 2
Jacobians of Transformations p. 12
Integration p. 18
Zonal Polynomials p. 29
Hypergeometric Functions of Matrix Argument p. 34
Laguerre Polynomials p. 41
Generalized Hermite Polynomials p. 42
(更多)
Preliminaries p. 1
Introduction p. 1
Matrix Algebra p. 2
Jacobians of Transformations p. 12
Integration p. 18
Zonal Polynomials p. 29
Hypergeometric Functions of Matrix Argument p. 34
Laguerre Polynomials p. 41
Generalized Hermite Polynomials p. 42
Notion of Random Matrix p. 44
Problems p. 47
Matrix Variate Normal Distribution p. 55
Introduction p. 55
Density Function p. 55
Properties p. 56
Singular Matrix Variate Normal Distribution p. 68
Symmetric Matrix Variate Normal Distribution p. 70
Restricted Matrix Variate Normal Distribution p. 74
Matrix Variate [theta]-Generalized Normal Distribution p. 77
Problems p. 82
Wishart Distribution p. 87
Introduction p. 87
Density Function p. 87
Properties p. 90
Inverted Wishart Distribution p. 111
Noncentral Wishart Distribution p. 113
Matrix Variate Gamma Distribution p. 122
Approximations p. 124
Problems p. 127
Matrix Variate t-Distribution p. 133
Introduction p. 133
Density Function p. 134
Properties p. 135
Inverted matrix Variate t-Distribution p. 142
Disguised Matrix Variate t-Distribution p. 143
Restricted Matrix Variate t-Distribution p. 151
Noncentral Matrix Variate t-Distribution p. 152
Distribution of Quadratic Forms p. 156
Problems p. 159
Matrix Variate Beta Distributions p. 165
Introduction p. 165
Density Functions p. 165
Properties p. 171
Related Distributions p. 182
Noncentral Matrix Variate Beta
Distribution p. 188
Problems p. 193
Matrix Variate Dirichlet Distributions p. 199
Introduction p. 199
Density Functions p. 199
Properties p. 204
Related Distributions p. 214
Noncentral Matrix Variate Dirichlet Distributions p. 218
Problems p. 222
Distribution of Quadratic Forms p. 225
Introduction p. 225
Density Function p. 225
Properties p. 228
Functions of Quadratic Forms p. 233
Series Representation of the Density p. 238
Noncentral Density Function p. 246
Expected Values p. 251
Wishartness and Independence of Quadratic Forms of The Type XAX' p. 253
Wishartness and Independence of Quadratic Forms of The Type XAX' + 1/2(LX' + XL') + C p. 262
Wishartness and Independence of Quadratic Forms of the Type XAX' + L[subscript 1]X' + XL'[subscript 2] + C p. 270
Problems p. 273
Miscellaneous Distributions p. 279
Introduction p. 279
Uniform Distribution on Stiefel Manifold p. 279
Von Mises-Fisher Distribution p. 281
Bingham Matrix Distribution p. 284
Generalized Bingham-Von Mises Matrix Distribution p. 285
Manifold Normal Distribution p. 287
Matrix Angular Central Gaussian Distribution p. 288
Bimatrix Wishart Distribution p. 289
Beta-Wishart Distribution p. 290
Confluent Hypergeometric Function Kind 1 Distribution p. 291
Confluent Hypergeometric Function Kind 2 Distribution p. 295
Hypergeometric Function Distributions p. 298
Generalized Hypergeometric Function Distributions p. 301
Complex Matrix Variate Distributions p. 303
Problems p. 304
General Families of Matrix Variate Distributions p. 311
Introduction p. 311
Matrix Variate Liouville Distributions p. 311
Matrix Variate Spherical Distributions p. 315
Matrix Variate Elliptically Contoured Distributions p. 322
Orthogonally Invariant and Residual Independent Matrix Distributions p. 323
Problems p. 328
Glossary of Notations and Abbreviations p. 331
References p. 343
Subject Index p. 364