Order statistics:
This volume provides an up-to-date coverage of the theory and applications of ordered random variables and their functions. Furthermore, it develops the distribution theory of OS systematically. Applications include procedures for the treatment of outliers and other data analysis techniques. Even wh...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Hoboken, New Jersey
Wiley-Interscience
2003
|
| Ausgabe: | Third edition |
| Schriftenreihe: | Wiley series in probability and statistics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | This volume provides an up-to-date coverage of the theory and applications of ordered random variables and their functions. Furthermore, it develops the distribution theory of OS systematically. Applications include procedures for the treatment of outliers and other data analysis techniques. Even when chapter and section headings are the same as in OSII, there are appreciable changes, mostly additions, with some obvious deletions. Parts of old Ch. 7, for example, are prime candidates for omission. Appendices are designed to help collate tables, computer algorithms, and software, as well as to compile related monographs on the subject matter. Extensive exercise sets will continue, many of them replaced by newer ones. |
| Beschreibung: | xv, 458 Seiten Diagramme |
| ISBN: | 0471389269 |
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Datensatz im Suchindex
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| adam_text | ORDER STATISTICS THIRD EDITION H. A. DAVID IOWA STATE UNIVERSITY
DEPARTMENT OF STATISTICS AMES, IA H. N. NAGARAJA THE OHIO STATE
UNIVERSITY DEPARTMENT OF STATISTICS COLUMBUS, OH IWILEY- INTERSCIENCE A
JOHN WILEY & SONS, INC., PUBLICATION CONTENTS PREFACE XI 1 INTRODUCTION
1 1.1 THE SUBJECT OF ORDER STATISTICS 1 1.2 THE SCOPE AND LIMITS OF THIS
BOOK 3 1.3 NOTATION 4 1.4 EXERCISES 7 2 BASIC DISTRIBUTION THEORY 9 2.1
DISTRIBUTION OF A SINGLE ORDER STATISTIC 9 2.2 JOINT DISTRIBUTION OF TWO
OR MORE ORDER STATISTICS 11 2.3 DISTRIBUTION OF THE RANGE AND OF OTHER
SYSTEMATIC STATISTICS 13 2.4 ORDER STATISTICS FOR A DISCRETE PARENT 16
2.5 CONDITIONAL DISTRIBUTIONS, ORDER STATISTICS AS A MARKOV CHAIN, AND
INDEPENDENCE RESULTS 17 2.6 RELATED STATISTICS 20 2. 7 EXERCISES 22 3
EXPECTED VALUES AND MOMENTS 33 3.1 BASIC FORMULAE 33 3.2 SPECIAL
CONTINUOUS DISTRIBUTIONS 40 VII VIII CONTENTS 3.3 THE DISCRETE CASE 42
3.4 RECURRENCE RELATIONS 44 3.5 EXERCISES 49 4 BOUNDS AND APPROXIMATIONS
FOR MOMENTS OF ORDER STATISTICS 59 4.1 INTRODUCTION 59 4.2
DISTRIBUTION-FREE BOUNDS FOR THE MOMENTS OF ORDER STATISTICS AND OF THE
RANGE 60 4.3 BOUNDS AND APPROXIMATIONS BY ORTHOGONAL INVERSE EXPANSION
70 4.4 STOCHASTIC ORDERINGS 74 4.5 BOUNDS FOR THE EXPECTED VALUES OF
ORDER STATISTICS IN TERMS OF QUANTILES OF THE PARENT DISTRIBUTION 80 4.6
APPROXIMATIONS TO MOMENTS IN TERMS OF THE QUANTILE FUNCTION AND ITS
DERIVATIVES 83 4.7 EXERCISES 86 5 THE NON-IID CASE 95 5.1 INTRODUCTION
95 5.2 ORDER STATISTICS FOR INDEPENDENT NONIDENTICALLY DISTRIBUTED
VARIATES 96 5.3 ORDER STATISTICS FOR DEPENDENT VARIATES 99 5.4
INEQUALITIES AND RECURRENCE RELATIONS * NON-IID CASES 102 5.5 BOUNDS FOR
LINEAR FUNCTIONS OF ORDER STATISTICS AND FOR THEIR EXPECTED VALUES 106
5.6 EXERCISES 113 6 FURTHER DISTRIBUTION THEORY 121 6.1 INTRODUCTION 121
6.2 STUDENTIZATION 122 6.3 STATISTICS EXPRESSIBLE AS MAXIMA 124 6.4
RANDOM DIVISION OF AN INTERVAL 133 6.5 LINEAR FUNCTIONS OF ORDER
STATISTICS 137 6.6 MOVING ORDER STATISTICS 140 CONTENTS IX 6.7
CHARACTERIZATIONS 142 6.8 CONCOMITANTS OF ORDER STATISTICS 144 6.9
EXERCISES 148 7 ORDER STATISTICS IN NONPARAMETRIC INFERENCE 159 7.1
DISTRIBUTION-FREE CONFIDENCE INTERVALS FOR QUANTILES 159 7.2
DISTRIBUTION-FREE TOLERANCE INTERVALS 164 7.3 DISTRIBUTION-FREE
PREDICTION INTERVALS 167 7.4 EXERCISES 169 8 ORDER STATISTICS IN
PARAMETRIC INFERENCE 171 8.1 INTRODUCTION AND BASIC RESULTS 171 8.2
INFORMATION IN ORDER STATISTICS 180 8.3 BOOTSTRAP ESTIMATION OF
QUANTILES AND OF MOMENTS OF ORDER STATISTICS 183 8.4 LEAST-SQUARES
ESTIMATION OF LOCATION AND SCALE PARAMETERS BY ORDER STATISTICS 185 8.5
ESTIMATION OF LOCATION AND SCALE PARAMETERS FOR CENSORED DATA 191 8.6
LIFE TESTING, WITH SPECIAL EMPHASIS ON THE EXPONENTIAL DISTRIBUTION 204
8.7 PREDICTION OF ORDER STATISTICS 208 8.8 ROBUST ESTIMATION 211 8.9
EXERCISES 223 9 SHORT-CUT PROCEDURES 239 9.1 INTRODUCTION 239 9.2 QUICK
MEASURES OF LOCATION 241 9.3 RANGE AND MEAN RANGE AS MEASURES OF
DISPERSION 243 9.4 OTHER QUICK MEASURES OF DISPERSION 248 9.5 QUICK
ESTIMATES IN BIVARIATE SAMPLES 250 9.6 THE STUDENTIZED RANGE 253 9.7
QUICK TESTS 257 9.8 RANKED-SET SAMPLING 262 X CONTENTS 9.9 O-STATISTICS
AND L-MOMENTS IN DATA SUMMARIZATION 268 9.10 PROBABILITY PLOTTING AND
TESTS OF GOODNESS OF FIT 2 70 9.11 STATISTICAL QUALITY CONTROL 2 74 9.12
EXERCISES 277 10 ASYMPTOTIC THEORY 283 10.1 INTRODUCTION 283 10.2
REPRESENTATIONS FOR THE CENTRAL SAMPLE QUANTILES 285 10.3 ASYMPTOTIC
JOINT DISTRIBUTION OF CENTRAL QUANTILES 288 10.4 OPTIMAL CHOICE OF ORDER
STATISTICS IN LARGE SAMPLES 290 10.5 THE ASYMPTOTIC DISTRIBUTION OF THE
EXTREME 296 10.6 THE ASYMPTOTIC JOINT DISTRIBUTION OF EXTREMES 306 10.7
EXTREME-VALUE THEORY FOR DEPENDENT SEQUENCES 309 10.8 ASYMPTOTIC
PROPERTIES OF INTERMEDIATE ORDER STATISTICS 311 10.9 ASYMPTOTIC RESULTS
FOR MULTIVARIATE SAMPLES 313 10.10 EXERCISES 315 11 ASYMPTOTIC RESULTS
FOR FUNCTIONS OF ORDER STATISTICS 323 11.1 INTRODUCTION 323 11.2
ASYMPTOTIC DISTRIBUTION OF THE RANGE, MIDRANGE, AND SPACINGS 324 11.3
LIMIT DISTRIBUTION OF THE TRIMMED MEAN 329 11.4 ASYMPTOTIC NORMALITY OF
LINEAR FUNCTIONS OF ORDER STATISTICS 331 11.5 OPTIMAL ASYMPTOTIC
ESTIMATION BY ORDER STATISTICS 335 11.6 ESTIMATORS OF TAIL INDEX AND
EXTREME QUANTILES 341 11.7 ASYMPTOTIC THEORY OF CONCOMITANTS OF ORDER
STATISTICS 345 11.8 EXERCISES 350 APPENDIX: GUIDE TO TABLES AND
ALGORITHMS 355 REFERENCES 367 INDEX 451
|
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| isbn | 0471389269 |
| language | English |
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| spelling | David, Herbert A. 1925- Verfasser (DE-588)119444798 aut Order statistics H. A. David ; H. N. Nagaraja Third edition Hoboken, New Jersey Wiley-Interscience 2003 xv, 458 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics This volume provides an up-to-date coverage of the theory and applications of ordered random variables and their functions. Furthermore, it develops the distribution theory of OS systematically. Applications include procedures for the treatment of outliers and other data analysis techniques. Even when chapter and section headings are the same as in OSII, there are appreciable changes, mostly additions, with some obvious deletions. Parts of old Ch. 7, for example, are prime candidates for omission. Appendices are designed to help collate tables, computer algorithms, and software, as well as to compile related monographs on the subject matter. Extensive exercise sets will continue, many of them replaced by newer ones. Statistik Ordnungsstatistik (DE-588)4212486-4 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Statistik (DE-588)4056995-0 s DE-604 Ordnungsstatistik (DE-588)4212486-4 s 1\p DE-604 Nagaraja, Haikady N. 1954- Verfasser (DE-588)104268697 aut HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013026580&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | David, Herbert A. 1925- Nagaraja, Haikady N. 1954- Order statistics Statistik Ordnungsstatistik (DE-588)4212486-4 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4212486-4 (DE-588)4056995-0 |
| title | Order statistics |
| title_auth | Order statistics |
| title_exact_search | Order statistics |
| title_full | Order statistics H. A. David ; H. N. Nagaraja |
| title_fullStr | Order statistics H. A. David ; H. N. Nagaraja |
| title_full_unstemmed | Order statistics H. A. David ; H. N. Nagaraja |
| title_short | Order statistics |
| title_sort | order statistics |
| topic | Statistik Ordnungsstatistik (DE-588)4212486-4 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Statistik Ordnungsstatistik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013026580&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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