Matrix variate distributions:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2000
|
| Schriftenreihe: | Chapman & Hall/CRC monographs and surveys in pure and applied mathematics
104 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 367 S. |
| ISBN: | 1584880465 9781584880462 |
Internformat
MARC
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| 100 | 1 | |a Gupta, Arjun K. |d 1938- |e Verfasser |0 (DE-588)122205103 |4 aut | |
| 245 | 1 | 0 | |a Matrix variate distributions |c A. K. Gupta ; D. K. Nagar |
| 264 | 1 | |a Boca Raton [u.a.] |b Chapman & Hall/CRC |c 2000 | |
| 300 | |a 367 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Chapman & Hall/CRC monographs and surveys in pure and applied mathematics |v 104 | |
| 650 | 4 | |a Analyse multivariée | |
| 650 | 4 | |a Distribution (Théorie des probabilités) | |
| 650 | 7 | |a Distribution (théorie des probabilités) - Analyse multivariée - Matrices aléatoires |2 ram | |
| 650 | 4 | |a Matrices aléatoires | |
| 650 | 7 | |a Matrices |2 gtt | |
| 650 | 7 | |a Multivariate analyse |2 gtt | |
| 650 | 4 | |a Distribution (Probability theory) | |
| 650 | 4 | |a Multivariate analysis | |
| 650 | 4 | |a Random matrices | |
| 650 | 0 | 7 | |a Multivariate Analyse |0 (DE-588)4040708-1 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Nagar, D. K. |e Verfasser |4 aut | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-008866111 | ||
Datensatz im Suchindex
| _version_ | 1804127710352506880 |
|---|---|
| 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
|
| any_adam_object | 1 |
| author | Gupta, Arjun K. 1938- Nagar, D. K. |
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| dewey-full | 519.2/4 |
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| dewey-ones | 519 - Probabilities and applied mathematics |
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| dewey-search | 519.2/4 |
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| id | DE-604.BV013009836 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:37:40Z |
| institution | BVB |
| isbn | 1584880465 9781584880462 |
| language | English |
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| series2 | Chapman & Hall/CRC monographs and surveys in pure and applied mathematics |
| spelling | Gupta, Arjun K. 1938- Verfasser (DE-588)122205103 aut Matrix variate distributions A. K. Gupta ; D. K. Nagar Boca Raton [u.a.] Chapman & Hall/CRC 2000 367 S. txt rdacontent n rdamedia nc rdacarrier Chapman & Hall/CRC monographs and surveys in pure and applied mathematics 104 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 rswk-swf Stochastische Matrix (DE-588)4057624-3 gnd rswk-swf Stochastische Matrix (DE-588)4057624-3 s Multivariate Analyse (DE-588)4040708-1 s DE-604 Nagar, D. K. Verfasser aut Chapman & Hall/CRC monographs and surveys in pure and applied mathematics 104 (DE-604)BV013350872 104 Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf 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 Inhaltsverzeichnis |
| 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 |
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