Elements of distribution theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2005
|
| Edition: | 1. publ. |
| Series: | Cambridge series in statistical and probabilistic mathematics
17 |
| Subjects: | |
| Online Access: | Klappentext Inhaltsverzeichnis |
| Physical Description: | XII, 515 S. graph. Darst. |
| ISBN: | 052184472X 9780521844727 9781107630734 |
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| adam_text | This detailed introduction to distribution theory uses no measure theory,
making it suitable for students in statistics and econometrics as well as for
researchers who use statistical methods. Good backgrounds in calculus
and linear algebra are important and a course in elementary mathematical
analysis is useful, but not required. An appendix gives a detailed summary
of the mathematical definitions and results that are used in the book.
Topics covered range from the basic distribution and density functions,
expectation, conditioning, characteristic functions,
in distribution, and the central limit theorem to more advanced concepts such
as exchangeability, models with a group structure, asymptotic approximations
to integrals, orthogonal polynomials, and saddlepoint approximations. The
emphasis is on topics useful in understanding statistical methodology; thus,
parametric statistical models and the distribution theory associated with the
normal distribution are covered comprehensively.
THOMAS
of Chicago. He is now a Professor of Statistics at Northwestern University.
He has also written Likelihood Methods in Statistics. He has published extensively
in statistical journals such as Biometrika, Journal of the American Statistical
Association, and Journal of the Royal Statistical Society. He is a member
of the Institute of Mathematical Statistics and the American Statistical
Association.
Cambridge Series in Statistical and Probabilistic Mathematics
Editorial Board:
R. Gill (Department of Mathematics. Utrecht University)
B.D.
S. Ross (Epstein Department of Industrial
University of Southern California)
B. W.
M. Stein (Department of Statistics. University of Chicago)
This series of high-quality upper-division textbooks and expository monographs
covers all aspects of stochastic applicable mathematics. The topics range from
pure and applied statistics to probability theory, operations research, optimiza¬
tion, and mathematical programming. The books contain clear presentations of
new developments in the field and also
While
¡contain
advances trf
CONTENTS PREFACE PAGE XI 1. PROPERTIES OF PROBABILITY DISTRIBUTIONS 1
1.1 INTRODUCTION 1 1.2 BASIC FRAMEWORK 1 1.3 RANDOM VARIABLES 5 1.4
DISTRIBUTION FUNCTIONS 8 1.5 QUANTILE FUNCTIONS 15 1.6 DENSITY AND
FREQUENCY FUNCTIONS 20 1.7 INTEGRATION WITH RESPECT TO A DISTRIBUTION
FUNCTION 26 1.8 EXPECTATION 28 1.9 EXERCISES 34 1.10 SUGGESTIONS FOR
FURTHER READING 38 2. CONDITIONAL DISTRIBUTIONS AND EXPECTATION 39 2.1
INTRODUCTION 39 39 46 53 59 62 64 67 2.2 2.3 2.4 2.5 2.6 2.7 2.8
MARGINAL DISTRIBUTIONS AND INDEPENDENCE CONDITIONAL DISTRIBUTIONS
CONDITIONAL EXPECTATION EXCHANGEABILITY MARTINGALES EXERCISES
SUGGESTIONS FOR FURTHER READING CHARACTERISTIC FUNCTIONS 3.1 3.2 3.3 3.4
3.5 INTRODUCTION BASIC PROPERTIES FURTHER PROPERTIES OF CHARACTERISTIC
FUNCTIONS EXERCISES SUGGESTIONS FOR FURTHER READING 3. CHARACTERISTIC
FUNCTIONS 69 69 72 82 90 93 4. MOMENTS AND CUMULANTS 94 4.1 INTRODUCTION
94 4.2 MOMENTS AND CENTRAL MOMENTS 94 4.3 LAPLACE TRANSFORMS AND
MOMENT-GENERATING FUNCTIONS 99 4.4 CUMULANTS 110 VLL VIII CONTENTS 4.5
MOMENTS AND CUMULANTS OF THE SAMPLE MEAN 120 4.6 CONDITIONAL MOMENTS AND
CUMULANTS 124 4.7 EXERCISES 127 4.8 SUGGESTIONS FOR FURTHER READING 130
5. PARAMETRIC FAMILIES OF DISTRIBUTIONS 132 5.1 INTRODUCTION 132 5.2
PARAMETERS AND IDENTIFIABILITY 132 5.3 EXPONENTIAL FAMILY MODELS 137 5.4
HIERARCHICAL MODELS 147 5.5 REGRESSION MODELS 150 5.6 MODELS WITH A
GROUP STRUCTURE 152 5.7 EXERCISES 164 5.8 SUGGESTIONS FOR FURTHER
READING 169 6. STOCHASTIC PROCESSES 170 6.1 INTRODUCTION 170 6.2
DISCRETE-TIME STATIONARY PROCESSES 171 6.3 MOVING AVERAGE PROCESSES 174
6.4 MARKOV PROCESSES 182 6.5 COUNTING PROCESSES 187 6.6 WIENER PROCESSES
192 6.7 EXERCISES 195 6.8 SUGGESTIONS FOR FURTHER READING 198 7.
DISTRIBUTION THEORY FOR FUNCTIONS OF RANDOM VARIABLES 199 7.1
INTRODUCTION 199 7.2 FUNCTIONS OF A REAL-VALUED RANDOM VARIABLE 199 7.3
FUNCTIONS OF A RANDOM VECTOR 202 7.4 SUMS OF RANDOM VARIABLES 212 7.5
ORDER STATISTICS 216 7.6 RANKS 224 7.7 MONTE CARLO METHODS 228 7.8
EXERCISES 231 7.9 SUGGESTIONS FOR FURTHER READING 234 8. NORMAL
DISTRIBUTION THEORY 235 8.1 INTRODUCTION 235 8.2 MULTIVARIATE NORMAL
DISTRIBUTION 235 8.3 CONDITIONAL DISTRIBUTIONS 240 8.4 QUADRATIC FORMS
244 8.5 SAMPLING DISTRIBUTIONS 250 8.6 EXERCISES 253 8.7 SUGGESTIONS FOR
FURTHER READING 256 9. APPROXIMATION OF INTEGRALS 257 9.1 INTRODUCTION
257 9.2 SOME USEFUL FUNCTIONS 257 9.3 ASYMPTOTIC EXPANSIONS 264 CONTENTS
IX 9.4 WATSON S LEMMA 268 9.5 LAPLACE S METHOD 276 9.6 UNIFORM
ASYMPTOTIC APPROXIMATIONS 281 9.7 APPROXIMATION OF SUMS 288 9.8
EXERCISES 295 9.9 SUGGESTIONS FOR FURTHER READING 297 10. ORTHOGONAL
POLYNOMIALS 299 10.1 INTRODUCTION 299 10.2 GENERAL SYSTEMS OF ORTHOGONAL
POLYNOMIALS 299 10.3 CLASSICAL ORTHOGONAL POLYNOMIALS 312 10.4 GAUSSIAN
QUADRATURE 317 10.5 EXERCISES 319 10.6 SUGGESTIONS FOR FURTHER READING
321 11. APPROXIMATION OF PROBABILITY DISTRIBUTIONS 322 11.1 INTRODUCTION
322 11.2 BASIC PROPERTIES OF CONVERGENCE IN DISTRIBUTION 325 11.3
CONVERGENCE IN PROBABILITY 338 11.4 CONVERGENCE IN DISTRIBUTION OF
FUNCTIONS OF RANDOM VECTORS 346 11.5 CONVERGENCE OF EXPECTED VALUES 349
11.6 OP AND O P NOTATION 354 11.7 EXERCISES 359 11.8 SUGGESTIONS FOR
FURTHER READING 364 12. CENTRAL LIMIT THEOREMS 365 12.1 INTRODUCTION 365
12.2 INDEPENDENT, IDENTICALLY DISTRIBUTED RANDOM VARIABLES 365 12.3
TRIANGULAR ARRAYS 367 12.4 RANDOM VECTORS 376 12.5 RANDOM VARIABLES WITH
A PARAMETRIC DISTRIBUTION 378 12.6 DEPENDENT RANDOM VARIABLES 386 12.7
EXERCISES 395 12.8 SUGGESTIONS FOR FURTHER READING 399 13.
APPROXIMATIONS TO THE DISTRIBUTIONS OF MORE GENERAL STATISTICS 400 13.1
INTRODUCTION 400 13.2 NONLINEAR FUNCTIONS OF SAMPLE MEANS 400 13.3 ORDER
STATISTICS 404 13.4 U -STATISTICS 415 13.5 RANK STATISTICS 422 13.6
EXERCISES 432 13.7 SUGGESTIONS FOR FURTHER READING 434 14. HIGHER-ORDER
ASYMPTOTIC APPROXIMATIONS 435 14.1 INTRODUCTION 435 14.2 EDGEWORTH
SERIES APPROXIMATIONS 435 CONTENTS 14.3 SADDLEPOINT APPROXIMATIONS 447
14.4 STOCHASTIC ASYMPTOTIC EXPANSIONS 454 14.5 APPROXIMATION OF MOMENTS
460 14.6 EXERCISES 466 14.7 SUGGESTIONS FOR FURTHER READING 469 APPENDIX
1. INTEGRATION WITH RESPECT TO A DISTRIBUTION FUNCTION 471 APPENDIX 2.
BASIC PROPERTIES OF COMPLEX NUMBERS 479 APPENDIX 3. SOME USEFUL
MATHEMATICAL FACTS 483 REFERENCES 503 NAME INDEX 507 SUBJECT INDEX 509
|
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| discipline | Mathematik Wirtschaftswissenschaften |
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| spelling | Severini, Thomas A. Verfasser aut Elements of distribution theory Thomas A. Severini 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2005 XII, 515 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge series in statistical and probabilistic mathematics 17 Verdelingen (statistiek) gtt Distribution (Probability theory) Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Wahrscheinlichkeitsverteilung (DE-588)4121894-2 s DE-604 Cambridge series in statistical and probabilistic mathematics 17 (DE-604)BV011442366 17 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013830731&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Klappentext SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013830731&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Severini, Thomas A. Elements of distribution theory Cambridge series in statistical and probabilistic mathematics Verdelingen (statistiek) gtt Distribution (Probability theory) Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd |
| subject_GND | (DE-588)4121894-2 (DE-588)4123623-3 |
| title | Elements of distribution theory |
| title_auth | Elements of distribution theory |
| title_exact_search | Elements of distribution theory |
| title_full | Elements of distribution theory Thomas A. Severini |
| title_fullStr | Elements of distribution theory Thomas A. Severini |
| title_full_unstemmed | Elements of distribution theory Thomas A. Severini |
| title_short | Elements of distribution theory |
| title_sort | elements of distribution theory |
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