Matrix Variate Distributions

 
 
Chapman and Hall (Verlag)
  • erschienen am 2. Mai 2018
  • |
  • 384 Seiten
 
E-Book | ePUB ohne DRM | Systemvoraussetzungen
978-1-351-43300-6 (ISBN)
 
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.
  • Englisch
  • Boca Raton
  • |
  • USA
Taylor & Francis Ltd
  • Für höhere Schule und Studium
  • |
  • Für Beruf und Forschung
644 equations
978-1-351-43300-6 (9781351433006)
weitere Ausgaben werden ermittelt
  • Cover
  • Half Title
  • Title Page
  • Copyright Page
  • Dedication
  • Preface
  • Table of Contents
  • 1: PRELIMINARIES
  • 1.1. INTRODUCTION
  • 1.2. MATRIX ALGEBRA
  • 1.3. JACOBIANS OF TRANSFORMATIONS
  • 1.4. INTEGRATION
  • 1.5. ZONAL POLYNOMIALS
  • 1.6. HYPERGEOMETRIC FUNCTIONS OF MATRIX ARGUMENT
  • 1.7. LAGUERRE POLYNOMIALS
  • 1.8. GENERALIZED HERMITE POLYNOMIALS
  • 1.9. NOTION OF RANDOM MATRIX
  • PROBLEMS
  • 2: MATRIX VARIATE NORMAL DISTRIBUTION
  • 2.1. INTRODUCTION
  • 2.2. DENSITY FUNCTION
  • 2.3. PROPERTIES
  • 2.4. SINGULAR MATRIX VARIATE NORMAL DISTRIBUTION
  • 2.5. SYMMETRIC MATRIX VARIATE NORMAL DISTRIBUTION
  • 2.6. RESTRICTED MATRIX VARIATE NORMAL DISTRIBUTION
  • 2.7. MATRIX VARIATE ?-GENERALIZED NORMAL DISTRIBUTION
  • PROBLEMS
  • 3: WISHART DISTRIBUTION
  • 3.1. INTRODUCTION
  • 3.2. DENSITY FUNCTION
  • 3.3. PROPERTIES
  • 3.4. INVERTED WISHART DISTRIBUTION
  • 3.5. NONCENTRAL WISHART DISTRIBUTION
  • 3.6. MATRIX VARIATE GAMMA DISTRIBUTION
  • 3.7. APPROXIMATIONS
  • PROBLEMS
  • 4: MATRIX VARIATE t-DISTRIBUTION
  • 4.1. INTRODUCTION
  • 4.2. DENSITY FUNCTION
  • 4.3. PROPERTIES
  • 4.4. INVERTED MATRIX VARIATE t-DISTRIBUTION
  • 4.5. DISGUISED MATRIX VARIATE t-DISTRIBUTION
  • 4.6. RESTRICTED MATRIX VARIATE t-DISTRIBUTION
  • 4.7. NONCENTRAL MATRIX VARIATE t-DISTRIBUTION
  • 4.8. DISTRIBUTION OF QUADRATIC FORMS
  • PROBLEMS
  • 5: MATRIX VARIATE BETA DISTRIBUTIONS
  • 5.1. INTRODUCTION
  • 5.2. DENSITY FUNCTIONS
  • 5.3. PROPERTIES
  • 5.4. RELATED DISTRIBUTIONS
  • 5.5. NONCENTRAL MATRIX VARIATE BETA DISTRIBUTION
  • PROBLEMS
  • 6: MATRIX VARIATE DIRICHLET DISTRIBUTIONS
  • 6.1. INTRODUCTION
  • 6.2. DENSITY FUNCTIONS
  • 6.3. PROPERTIES
  • 6.4. RELATED DISTRIBUTIONS
  • 6.5. NONCENTRAL MATRIX VARIATE DIRICHLET DISTRIBUTIONS
  • PROBLEMS
  • 7: DISTRIBUTION OF QUADRATIC FORMS
  • 7.1. INTRODUCTION
  • 7.2. DENSITY FUNCTION
  • 7.3. PROPERTIES
  • 7.4. FUNCTIONS OF QUADRATIC FORMS
  • 7.5. SERIES REPRESENTATION OF THE DENSITY
  • 7.6. NONCENTRAL DENSITY FUNCTION
  • 7.7. EXPECTED VALUES
  • 7.8. WISHARTNESS AND INDEPENDENCE OF QUADRATIC FORMS OF THE TYPE X A X'
  • 7.9. WISHARTNESS AND INDEPENDENCE OF QUADRATIC FORMS OF THE TYPE XAX' + 1/2(LX' + XL') + C
  • 7.10. WISHARTNESS AND INDEPENDENCE OF QUADRATIC FORMS OF THE TYPE XAX' + L1X' + XL2' + C
  • PROBLEMS
  • 8: MISCELLANEOUS DISTRIBUTIONS
  • 8.1. INTRODUCTION
  • 8.2. UNIFORM DISTRIBUTION ON STIEFEL MANIFOLD
  • 8.3. VON MISES-FISHER DISTRIBUTION
  • 8.4. BINGHAM MATRIX DISTRIBUTION
  • 8.5. GENERALIZED BINGHAM-VON MISES MATRIX DISTRIBUTION
  • 8.6. MANIFOLD NORMAL DISTRIBUTION
  • 8.7. MATRIX ANGULAR CENTRAL GAUSSIAN DISTRIBUTION
  • 8.8. BIMATRIX WISHART DISTRIBUTION
  • 8.9. BETA-WISHART DISTRIBUTION
  • 8.10. CONFLUENT HYPERGEOMETRIC FUNCTION KIND 1 DISTRIBUTION
  • 8.11. CONFLUENT HYPERGEOMETRIC FUNCTION KIND 2 DISTRIBUTION
  • 8.12. HYPERGEOMETRIC FUNCTION DISTRIBUTIONS
  • 8.13. GENERALIZED HYPERGEOMETRIC FUNCTION DISTRIBUTIONS
  • 8.14. COMPLEX MATRIX VARIATE DISTRIBUTIONS
  • PROBLEMS
  • 9: GENERAL FAMILIES OF MATRIX VARIATE DISTRIBUTIONS
  • 9.1. INTRODUCTION
  • 9.2. MATRIX VARIATE LIOUVILLE DISTRIBUTIONS
  • 9.3. MATRIX VARIATE SPHERICAL DISTRIBUTIONS
  • 9.4. MATRIX VARIATE ELLIPTICALLY CONTOURED DISTRIBUTIONS
  • 9.5. ORTHOGONALLY INVARIANT AND RESIDUAL INDEPENDENT MATRIX DISTRIBUTIONS
  • PROBLEMS
  • GLOSSARY OF NOTATIONS AND ABBREVIATIONS
  • REFERENCES
  • SUBJECT INDEX

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