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Matrix Variate Distributions [electronic resource].

By: Gupta, A. K.
Contributor(s): Nagar, D. K.
Material type: materialTypeLabelBookSeries: Publisher: Boca Raton : Chapman and Hall/CRC, 2018Description: 1 online resource (385 p.).Content type: text Media type: computer Carrier type: online resourceISBN: 9781351433006; 1351433008; 9781351433013; 1351433016.Subject(s): MATHEMATICS / Applied | MATHEMATICS / Probability & Statistics / GeneralDDC classification: 519.2/4 Online resources: Click here to view. | OCLC metadata license agreement
Contents:
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
4.7. NONCENTRAL MATRIX VARIATE t-DISTRIBUTION4.8. 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 FORMS7.5. 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 DISTRIBUTION8.6. 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
Abstract: 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 distributionWishart distributionMatrix variate t-distributionMatrix variate beta distributionF-distributionMatrix variate Dirichlet distributionMatrix quadratic formsWith its inclusion of new results, Matrix Variate Distributions promises to stimulate further research and help advance the field of multivariate statistical analysis.
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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

4.7. NONCENTRAL MATRIX VARIATE t-DISTRIBUTION4.8. 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 FORMS7.5. 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 DISTRIBUTION8.6. 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

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 distributionWishart distributionMatrix variate t-distributionMatrix variate beta distributionF-distributionMatrix variate Dirichlet distributionMatrix quadratic formsWith its inclusion of new results, Matrix Variate Distributions promises to stimulate further research and help advance the field of multivariate statistical analysis.

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