CRC handbook of tables for the use of order statistics in estimation:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
CRC Press
1996
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Gleichzeitig Revision von: Order statistics and their use in testing and estimation. Vol. 2 |
| Beschreibung: | XVII, 669 S. graph. Darst. |
| ISBN: | 084939452X |
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Datensatz im Suchindex
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|---|---|
| adam_text | CRC HANDBOOK OF TAHLES FOR THE USE OF ORDER STATISTICS IN ESTIRNATION H.
LEON HARTER CHAMPAIGN, ILLINOIS N. BALAKRISHNAN DEPARTMENT OF
MATHEMATICS AND STATISTICS MCMASTER UNIVERSITY ONTARIO, CANADA W CRC
PRESS BOCARATON NEW YORK LONDON TOKYO CONTENTS PREFACE V LIST OF TABLES
XV INTRODUCTION 1 1 QUASI-RANGES OF SAMPLES FROM A NORMAL POPULATION 5
1.1 POINT ESTIMATION OF THE POPULATION STANDARD DEVIATION A, 5 1.1.1
INTRODUCTION, 5 1.1.2 METHOD OF COMPUTATION OF AUXILIARY TABLES, 6 1.1.3
UNBIASED ESTIMATORS OF ER, 7 1.1.4 COMPARISON WITH GRUBBS-WEAVER
ESTIMATORS, 9 1.1.5 NUMERICAL EXAMPLE, 11 1.1.6 REFERENCES, 11 1.2
INTERVAL ESTIMATION OF THE POPULATION STANDARD DEVIATION ER, 13 1.2.1
INTRODUCTION, 13 1.2.2 CRITERIA FOR BEST SUBSTITUTE INTERVAL ESTIMATORS,
14 1.2.3 MATHEMATICAL FORMULATION, 17 1.2.4 METHOD OF COMPUTATION OF THE
TABLES, 19 1.2.5 COMPARISON WITH OTHER TABLES, 22 1.2.6 REFERENCES, 23 2
THE RANGE OF SAMPLES FROM A RECTANGULAR POPULATION 25 2.1 POINT
ESTIMATION OF THE POPULATION STANDARD DEVIATION ER, 25 2.1.1 UNBIASED
ESTIMATOR WHEN POPULATION IS KNOWN TO BE RECTANGULAR, 25 2.1.2 BIAS WHEN
ESTIMATORS WHICH ASSUME NORMALITY ARE USED, 26 2.1.3 REFERENCES, 26 2.2
INTERVAL ESTIMATION OF THE POPULATION STANDARD DEVIATION A, 27 2.2.1
INTRODUCTION, 27 2.2.2 METHOD OF COMPUTATION OF THE TABLES, 27 2.2.3
EFFECTIVENESS OF CONFIDENCE INTERVALS, 29 2.2.4 EXAMPLE, 29 2.2.5
REFERENCES, 29 3 EXPECTED VALUES, VARIANCES AND COVARIANCES OF ORDER
STATISTICS OF SAMPLES FROM VARIOUS POPULATIONS 3.1 NORMAL POPULATION, 31
3.1.1 HISTORY, 31 3.1.2 METHOD OF COMPUTATION OF TABLES OF EXPECTED
VALUES, 34 3.1.3 BLOM S APPROXIMATION, 34 3.1.4 APPLICATIONS OF TABLES
OF EXPECTED VALUES, 36 3.1.5 METHOD OF COMPUTATION OF TABLES OF
VARIANCES AND COVARIANCES, 36 3.1.6 APPLICATIONS OF TABLES OF VARIANCES
AND COVARIANCES, 37 3.1.7 REFERENCES, 38 3.2 EXPONENTIAL, WEIBULL AND
GAMMA POPULATIONS, 42 3.2.1 INTRODUCTION, 42 3.2.2 MATHEMATICAL
FORMULATIONS AND METHODS OF COMPUTATION, 42 3.2.3 USES OF TABLES OF
MEANS, 49 3.2.4 USES OF TABLES OF VARIANCES AND COVARIANCES, 54 3.2.5
REFERENCES, 57 3.3 OTHER POPULATIONS, 63 3.3.1 LOGNORMAL POPULATION, 63
3.3.2 LOG-WEIBULL POPULATION, 64 3.3.3 LOG-GAMMA POPULATION, 65 3.3.4
CAUCHY POPULATION, 66 3.3.5 DOUBLE EXPONENTIAL POPULATION, 67 3.3.6 HALF
NORMAL POPULATION, 68 3.3.7 LOGISTIC POPULATION, 69 3.3.8 PARETO
POPULATION, 70 3.3.9 STUDENT S T POPULATION, 71 3.3.10 HALF LOGISTIC
POPULATION, 72 3.3.11 GENERALIZED LOGISTIC POPULATION, 73 3.3.12
APPLICATIONS OF TABLES, 74 3.3.13 REFERENCES, 81 4 ONE OR TWO ORDER
STATISTICS FROM AN EXPONENTIAL POPULATION 4.1 POINT ESTIMATION OF ONE OR
TWO PARAMETERS, 89 4.1.1 INTRODUCTION, 89 4.1.2 ESTIMATORS OF ER FOR THE
ONE-PARAMETER EXPONENTIAL POPULATION, 90 4.1.3 ESTIMATORS OF PARAMETERS
OF THE TWO-PARAMETER EXPONENTIAL POPULATION, 92 4.1.4 REMARKS, 94 4.1.5
REFERENCES, 95 4.2 INTERVAL ESTIMATION OF THE PARAMETER A, 96 4.2.1
INTRODUCTION, 96 4.2.2 MATHEMATICAL FORMULATION, 97 4.2.3 METHOD OF
COMPUTATION OF TABLES, 100 4.2.4 COMPARISON WITH OTHER TABLES, 102 4.2.5
POSSIBLE USES OF THE TABLES, 102 4.2.6 NUMERICAL EXAMPLE, 103 4.2.7
REFERENCES, 103 5 SINGLY CENSORED SAMPLES FROM POPULATIONS RELATED TO
THE EXPONENTIAL 5.1 WEIBULL POPULATIONS WITH KNOWN LOCATION AND SHAPE
PARAMETERS, 105 5.1.1 INTRODUCTION, 105 5.1.2 POINT ESTIMATION OF THE
SCALE PARAMETER 9, 105 5.1.3 INTERVAL ESTIMATION OF THE SCALE PARAMETER
8, 107 5.1.4 NUMERICAL EXAMPLE, 109 5.1.5 REFERENCES, 109 5.2 TYPE I
EXTREME-VALUE POPULATION WITH KNOWN SCALE PARAMETER, 111 5.2.1
INTRODUCTION, 111 5.2.2 POINT ESTIMATION OF THE LOCATION PARAMETER U,
111 5.2.3 INTERVAL ESTIMATION OF THE LOCATION PARAMETER U, 114 5.2.4
NUMERICAL EXAMPLE, 114 5.2.5 REFERENCES, 115 5.3 TYPE II EXTREME-VALUE
POPULATIONS WITH KNOWN SHAPE PARAMETERS, 117 5.3.1 INTRODUCTION, 117
5.3.2 POINT ESTIMATION OF THE SCALE PARAMETERS V N AND V , 117 5.3.3
INTERVAL ESTIMATION OF THE SCALE PARAMETERS V N AND V , 120 5.3.4
NUMERICAL EXAMPLE, 120 5.3.5 REMARKS ON APPLICATIONS, 121 5.3.6
REFERENCES, 121 5.4 PARETO AND LIMITED POPULATIONS WITH KNOWN LOCATION
PARAMETERS, 123 5.4.1 INTRODUCTION, 123 5.4.2 POINT ESTIMATION OF THE
SHAPE PARAMETER K , 123 5.4.3 INTERVAL ESTIMATION OF THE SHAPE
PARAMETERS K, 126 5.4.4 NUMERICAL EXAMPLES, 126 5.4.5 REFERENCES, 127 XU
6 SINGLE ORDER STATISTICS PROM POPULATIONS RELATED TO THE EXPONENTIAL
129 6.1 WEIBULL POPULATION WITH KNOWN LOCATION AND SHAPE PARAMETERS, 129
6.1.1 INTRODUCTION, 129 6.1.2 POINT ESTIMATION OF THE SCALE PARAMETER 9,
129 6.1.3 INTERVAL ESTIMATION OF THE SCALE PARAMETER 9, 132 6.1.4 USEOF
TABLES, 132 6.1.5 NUMERICAL EXAMPLE, 133 6.1.6 REFERENCES, 133 6.2 TYPE
I EXTREME-VALUE POPULATION WITH KNOWN SCALE PARAMETER, 135 6.2.1
INTRODUCTION, 135 6.2.2 POINT ESTIMATION OF THE LOCATION PARAMETER U,
135 6.2.3 INTERVAL ESTIMATION OF THE LOCATION PARAMETER U, 136 6.2.4 USE
OF TABLES, 137 6.2.5 NUMERICAL EXAMPLE, 137 6.2.6 REFERENCES, 138 6.3
TYPE II EXTREME-VALUE POPULATIONS WITH KNOWN SHAPE PARAMETERS, 139 6.3.1
INTRODUCTION, 139 6.3.2 POINT ESTIMATION OF THE SCALE PARAMETERS V AND
V N , 139 6.3.3 INTERVAL ESTIMATION OF SCALE PARAMETERS V AND V N , 140
6.3.4 NUMERICAL EXAMPLE, 141 6.3.5 REMARKS ON APPLICATIONS, 142 6.3.6
REFERENCES, 142 6.4 LIMITED AND PARETO POPULATIONS WITH KNOWN LOCATION
PARAMETERS, 143 6.4.1 INTRODUCTION, 143 6.4.2 POINT ESTIMATION OF THE
SHAPE PARAMETERS K, 143 6.4.3 INTERVAL ESTIMATION OF SHAPE PARAMETERS K,
144 6.4.4 NUMERICAL EXAMPLES, 145 6.4.5 REFERENCES, 147 7 DOUBLY
CENSORED SAMPLES FRORN VARIOUS POPULATIONS 149 7.1 MAXIMUM-LIKELIHOOD
ESTIMATION OF TWO PARAMETERS OF NORMAL POPULATION, 149 7.1.1
INTRODUCTION, 149 7.1.2 MATHEMATICAL FORMULATION, 150 7.1.3 ASYMPTOTIC
VARIANCES AND COVARIANCES, 151 7.1.4 ITERATIVE ESTIMATION PROCEDURE, 153
7.1.5 MONTE CARLO STUDY FOR SMALL SAMPLES, 153 7.1.6 REFERENCES, 154 7.2
LOCAL-MAXIMUM-LIKELIHOOD ESTIMATION OF THREE PARAMETERS OF LOGNORMAL
POPULATION, 156 XIII 7.2.1 INTRODUCTION, 156 7.2.2 THE LIKELIHOOD
EQUATIONS, 157 7.2.3 ASYMPTOTIE VARIANCES AND COVARIANCES, 158 7.2.4
ITERATIVE ESTIMATION PROCEDURE, 160 7.2.5 MONTE CARLO STUDY FOR SAMPLES
OF MODERATE SIZE, 161 7.2.6 REFERENCES, 162 7.3 MAXIMUM-LIKELIHOOD
ESTIMATION OF THREE PARAMETERS OF WEIBULL AND GAMMA POPULATIONS, 164
7.3.1 INTRODUCTION, 164 7.3.2 MATHEMATICAL FORMULATION, 165 7.3.3
ITERATIVE ESTIMATION PROCEDURE, 166 7.3.4 NUMERICAL EXAMPLES, 167 7.3.5
ASYMPTOTIE VARIANCES AND COVARIANCES, 167 7.3.6 MONTE CARLO STUDY FOR
SAMPLES OF MODERATE SIZE, 172 7.3.7 REMARKS ON REGULAER AND NON-REGULAR
ESTIMATION, 172 7.3.8 REFERENCES, 173 7.4 MAXIMUM-LIKELIHOOD ESTIMATION
OF TWO PARAMETERS OF LOGISTIC POPULATIONS, 176 7.4.1 INTRODUCTION, 176
7.4.2 THE LIKELIHOOD FUNCTION AND ITS DERIVATIVES, 176 7.4.3 ASYMPTOTIE
VARIANCES AND COVARIANCES, 177 7.4.4 ITERATIVE ESTIMATION PROCEDURE, 179
7.4.5 MONTE CARLO STUDY FOR SMALL SAMPLES, 179 7.4.6 NUMERICAL EXAMPLES,
180 7.4.7 REFERENCES, 181 7.5 MAXIMUM-LIKELIHOOD ESTIMATION OF TWO
PARAMETERS OF TYPE I EXTREME-VALUE POPULATION, 183 7.5.1 INTRODUCTION,
183 7.5.2 THE LIKELIHOOD FUNCTION AND ITS DERIVATIVES, 185 7.5.3
ASYMPTOTIE VARIANCES AND COVARIANCES, 186 7.5.4 ITERATIVE ESTIMATION
PROCEDURE, 187 7.5.5 MONTE CARLO STUDY FOR SMALL SAMPLES, 187 7.5.6
NUMERICAL EXAMPLE, 188 7.5.7 REFERENCES, 189 7.6 MAXIMUM-LIKELIHOOD
ESTIMATION OF TWO PARAMETERS OF LOG-GAMMA POPULATION, 193 7.6.1
INTRODUCTION, 193 7.6.2 THE LOG-GAMMA POPULATION, 193 7.6.3 THE
LIKELIHOOD FUNCTION AND ITS DERIVATIVES, 195 7.6.4 MAXIMUM-LIKELIHOOD
INFORMATION MATRIX, 196 . 7.6.5 ASYMPTOTIE VARIANCES AND COVARIANCES,
197 7.6.6 ITERATIVE ESTIMATION PROCEDURE AND MONTE CARLO STUDY, 198
7.6.7 NUMERICAL EXAMPLE, 199 7.6.8 REFERENCES, 199 XIV 7.7
MAXIMUM-LIKELIHOOD ESTIMATION OF THREE PARAMETERS OF GENERALIZED
EXTREME-VALUE POPULATION, 201 7.7.1 INTRODUCTION, 201 7.7.2
THE-LIKELIHOOD EQUATIONS, 201 7.7.3 THE ITERATIVE METHOD, 202 7.7.4
CALCULATION OF V(A^), 203 7.7.5 VARIANCES AND COVARIANCES OF THE
ESTIMATORS, 205 7.7.6 REFERENCES, 206 7.8 REMARKS ON INTERVAL ESTIMATION
OF PARAMETERS OF ABOVE POPULATIONS, 208 7.8.1 CONFIDENCE BOUNDS FOR
INDIVIDUAL PARAMETERS, 208 7.8.2 CONFIDENCE ELLIPSOIDS FOR SETS OF
PARAMETERS, 208 APPENDIX A 209 APPENDIX B 309 APPENDIX C 323 APPENDIX D
531 APPENDIX E 571 APPENDIX F 603 APPENDIX G 629 SUBJECT INDEX 659
AUTHOR INDEX 665
|
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| spellingShingle | Harter, Harman Leon Balakrishnan, Narayanaswamy 1956- CRC handbook of tables for the use of order statistics in estimation Statistiques ordonnées - Tables Order statistics Tables Schätzung (DE-588)4193791-0 gnd Ordnungsstatistik (DE-588)4212486-4 gnd |
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| title | CRC handbook of tables for the use of order statistics in estimation |
| title_auth | CRC handbook of tables for the use of order statistics in estimation |
| title_exact_search | CRC handbook of tables for the use of order statistics in estimation |
| title_full | CRC handbook of tables for the use of order statistics in estimation H. Leon Harter ; N. Balakrishnan |
| title_fullStr | CRC handbook of tables for the use of order statistics in estimation H. Leon Harter ; N. Balakrishnan |
| title_full_unstemmed | CRC handbook of tables for the use of order statistics in estimation H. Leon Harter ; N. Balakrishnan |
| title_short | CRC handbook of tables for the use of order statistics in estimation |
| title_sort | crc handbook of tables for the use of order statistics in estimation |
| topic | Statistiques ordonnées - Tables Order statistics Tables Schätzung (DE-588)4193791-0 gnd Ordnungsstatistik (DE-588)4212486-4 gnd |
| topic_facet | Statistiques ordonnées - Tables Order statistics Tables Schätzung Ordnungsstatistik Tabelle |
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