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Bibliographic Details
Main Authors:	David, Herbert A. 1925- (Author), Nagaraja, Haikady N. 1954- (Author)
Format:	Book
Language:	English
Published:	Hoboken, New Jersey Wiley-Interscience 2003
Edition:	Third edition
Series:	Wiley series in probability and statistics
Subjects:	Statistik Ordnungsstatistik
Links:	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
Abstract:	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.
Physical Description:	xv, 458 Seiten Diagramme
ISBN:	0471389269

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Record in the Search Index

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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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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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