Cover Image

Matrix variate distributions / A.K. Gupta, D.K. Nagar.

Show other versions (1)

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...

Full description

Saved in:
Bibliographic Details
Online Access: Full Text (via Taylor & Francis)
Main Author: Gupta, A. K. (Arjun K.), 1938-
Other Authors: Nagar, D. K.
Format: eBook
Language:English
Published: Boca Raton, FL : Chapman & Hall, ©2000.
Series:Chapman & Hall/CRC monographs and surveys in pure and applied mathematics ; 104.
Subjects:
Distribution (Probability theory)
Multivariate analysis.
Random matrices.
Table of Contents:
  • 1 Preliminaries 1
  • 1.2. Matrix Algebra 2
  • 1.3. Jacobians of Transformations 12
  • 1.4. Integration 18
  • 1.5. Zonal Polynomials 29
  • 1.6. Hypergeometric Functions of Matrix Argument 34
  • 1.7. Laguerre Polynomials 41
  • 1.8. Generalized Hermite Polynomials 42
  • 1.9. Notion of Random Matrix 44
  • 2 Matrix Variate Normal Distribution 55
  • 2.2. Density Function 55
  • 2.3. Properties 56
  • 2.4. Singular Matrix Variate Normal Distribution 68
  • 2.5. Symmetric Matrix Variate Normal Distribution 70
  • 2.6. Restricted Matrix Variate Normal Distribution 74
  • 2.7. Matrix Variate [theta]-Generalized Normal Distribution 77
  • 3 Wishart Distribution 87
  • 3.2. Density Function 87
  • 3.3. Properties 90
  • 3.4. Inverted Wishart Distribution 111
  • 3.5. Noncentral Wishart Distribution 113
  • 3.6. Matrix Variate Gamma Distribution 122
  • 3.7. Approximations 124
  • 4 Matrix Variate t-Distribution 133
  • 4.2. Density Function 134
  • 4.3. Properties 135
  • 4.4. Inverted matrix Variate t-Distribution 142
  • 4.5. Disguised Matrix Variate t-Distribution 143
  • 4.6. Restricted Matrix Variate t-Distribution 151
  • 4.7. Noncentral Matrix Variate t-Distribution 152
  • 4.8. Distribution of Quadratic Forms 156
  • 5 Matrix Variate Beta Distributions 165
  • 5.2. Density Functions 165
  • 5.3. Properties 171
  • 5.4. Related Distributions 182
  • 5.5. Noncentral Matrix Variate Beta
  • Distribution 188
  • 6 Matrix Variate Dirichlet Distributions 199
  • 6.2. Density Functions 199
  • 6.3. Properties 204
  • 6.4. Related Distributions 214
  • 6.5. Noncentral Matrix Variate Dirichlet Distributions 218
  • 7 Distribution of Quadratic Forms 225
  • 7.2. Density Function 225
  • 7.3. Properties 228
  • 7.4. Functions of Quadratic Forms 233
  • 7.5. Series Representation of the Density 238
  • 7.6. Noncentral Density Function 246
  • 7.7. Expected Values 251
  • 7.8. Wishartness and Independence of Quadratic Forms of The Type XAX' 253
  • 7.9. Wishartness and Independence of Quadratic Forms of The Type XAX' + 1/2(LX' + XL') + C 262
  • 7.10. Wishartness and Independence of Quadratic Forms of the Type XAX' + L[subscript 1]X' + XL'[subscript 2] + C 270
  • 8 Miscellaneous Distributions 279
  • 8.2. Uniform Distribution on Stiefel Manifold 279
  • 8.3. Von Mises-Fisher Distribution 281
  • 8.4. Bingham Matrix Distribution 284
  • 8.5. Generalized Bingham-Von Mises Matrix Distribution 285
  • 8.6. Manifold Normal Distribution 287
  • 8.7. Matrix Angular Central Gaussian Distribution 288
  • 8.8. Bimatrix Wishart Distribution 289
  • 8.9. Beta-Wishart Distribution 290
  • 8.10. Confluent Hypergeometric Function Kind 1 Distribution 291
  • 8.11. Confluent Hypergeometric Function Kind 2 Distribution 295
  • 8.12. Hypergeometric Function Distributions 298
  • 8.13. Generalized Hypergeometric Function Distributions 301
  • 8.14. Complex Matrix Variate Distributions 303
  • 9 General Families of Matrix Variate Distributions 311
  • 9.2. Matrix Variate Liouville Distributions 311
  • 9.3. Matrix Variate Spherical Distributions 315
  • 9.4. Matrix Variate Elliptically Contoured Distributions 322
  • 9.5. Orthogonally Invariant and Residual Independent Matrix Distributions 323.

Similar Items