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Matrix Variate Distributions.

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Bibliographic Details
Main Author: Gupta, A. K.
Corporate Author: Taylor & Francis
Other Authors: Nagar, D. K.
Format: eBook
Language:English
Published: Boca Raton : Chapman and Hall/CRC, 2018.
Series:Monographs and Surveys in Pure and Applied Mathematics Ser. ; v.104
Subjects:
MATHEMATICS / Applied.
MATHEMATICS / Probability & Statistics / General.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of 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