Verfügbarkeit: Matrix variate distributions | Technische Universität München

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Bibliographische Detailangaben
Beteiligte Personen:	Gupta, Arjun K. 1938- (VerfasserIn), Nagar, D. K. (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Boca Raton [u.a.] Chapman & Hall/CRC 2000
Schriftenreihe:	Chapman & Hall/CRC monographs and surveys in pure and applied mathematics 104
Schlagwörter:	Analyse multivariée Distribution (Théorie des probabilités) Distribution (théorie des probabilités) - Analyse multivariée - Matrices aléatoires Matrices aléatoires Matrices Multivariate analyse Distribution (Probability theory) Multivariate analysis Random matrices Multivariate Analyse Stochastische Matrix
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008866111&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	367 S.
ISBN:	1584880465 9781584880462

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Datensatz im Suchindex

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adam_text	TABLE OF CONTENTS 1 PRELIMINARIES 1 1.1. INTRODUCTION 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 PROBLEMS 47 2 MATRIX VARIATE NORMAL DISTRIBUTION 55 2.1. INTRODUCTION 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 ^-GENERALIZED NORMAL DISTRIBUTION 77 PROBLEMS 82 3 WISHART DISTRIBUTION 87 3.1. INTRODUCTION 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 PROBLEMS 127 4 MATRIX VARIATE ¿-DISTRIBUTION 133 4.1. INTRODUCTION 133 4.2. DENSITY FUNCTION 134 4.3. PROPERTIES 135 4.4. INVERTED MATRIX VARIATE ¿-DISTRIBUTION 142 4.5. DISGUISED MATRIX VARIATE ¿-DISTRIBUTION 143 4.6. RESTRICTED MATRIX VARIATE ¿-DISTRIBUTION 151 4.7. NONCENTRAL MATRIX VARIATE ¿-DISTRIBUTION 152 4.8. DISTRIBUTION OF QUADRATIC FORMS 156 PROBLEMS 159 5 MATRIX VARIATE BETA DISTRIBUTIONS 165 5.1. INTRODUCTION 165 5.2. DENSITY FUNCTIONS 165 5.3. PROPERTIES 171 5.4. RELATED DISTRIBUTIONS 182 5.5. NONCENTRAL MATRIX VARIATE BETA DISTRIBUTION 188 PROBLEMS 193 6 MATRIX VARIATE DIRICHLET DISTRIBUTIONS 199 6.1. INTRODUCTION 199 6.2. DENSITY FUNCTIONS 199 6.3. PROPERTIES 204 6.4. RELATED DISTRIBUTIONS 214 6.5. NONCENTRAL MATRIX VARIATE DIRICHLET DISTRIBUTIONS 218 PROBLEMS 222 7 DISTRIBUTION OF QUADRATIC FORMS 225 7.1. INTRODUCTION 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 + i {LX + XL ) + C 262 7.10. WISHARTNESS AND INDEPENDENCE OF QUADRATIC FORMS OF THE TYPE XAX + LxX + XL 2 + C 270 PROBLEMS 273 8 MISCELLANEOUS DISTRIBUTIONS 279 8.1. INTRODUCTION 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 PROBLEMS 304 9 GENERAL FAMILIES OF MATRIX VARIATE DISTRIBUTIONS 311 9.1. INTRODUCTION 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 PROBLEMS 328 GLOSSARY OF NOTATIONS AND ABBREVIATIONS 331 REFERENCES 343 SUBJECT INDEX 364
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author	Gupta, Arjun K. 1938- Nagar, D. K.
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isbn	1584880465 9781584880462
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spellingShingle	Gupta, Arjun K. 1938- Nagar, D. K. Matrix variate distributions Chapman & Hall/CRC monographs and surveys in pure and applied mathematics Analyse multivariée Distribution (Théorie des probabilités) Distribution (théorie des probabilités) - Analyse multivariée - Matrices aléatoires ram Matrices aléatoires Matrices gtt Multivariate analyse gtt Distribution (Probability theory) Multivariate analysis Random matrices Multivariate Analyse (DE-588)4040708-1 gnd Stochastische Matrix (DE-588)4057624-3 gnd
subject_GND	(DE-588)4040708-1 (DE-588)4057624-3
title	Matrix variate distributions
title_auth	Matrix variate distributions
title_exact_search	Matrix variate distributions
title_full	Matrix variate distributions A. K. Gupta ; D. K. Nagar
title_fullStr	Matrix variate distributions A. K. Gupta ; D. K. Nagar
title_full_unstemmed	Matrix variate distributions A. K. Gupta ; D. K. Nagar
title_short	Matrix variate distributions
title_sort	matrix variate distributions
topic	Analyse multivariée Distribution (Théorie des probabilités) Distribution (théorie des probabilités) - Analyse multivariée - Matrices aléatoires ram Matrices aléatoires Matrices gtt Multivariate analyse gtt Distribution (Probability theory) Multivariate analysis Random matrices Multivariate Analyse (DE-588)4040708-1 gnd Stochastische Matrix (DE-588)4057624-3 gnd
topic_facet	Analyse multivariée Distribution (Théorie des probabilités) Distribution (théorie des probabilités) - Analyse multivariée - Matrices aléatoires Matrices aléatoires Matrices Multivariate analyse Distribution (Probability theory) Multivariate analysis Random matrices Multivariate Analyse Stochastische Matrix
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008866111&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV013350872
work_keys_str_mv	AT guptaarjunk matrixvariatedistributions AT nagardk matrixvariatedistributions

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