Estimation Methods
E-Book, Englisch, 399 Seiten
ISBN: 978-1-4832-9749-1
Verlag: Elsevier Reference Monographs
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)
Autoren/Hrsg.
Weitere Infos & Material
1;Front Cover
;1
2;Order Statistics and Inference:
Estimation Methods;4
3;Copyright Page;5
4;Table of Contents;8
5;Dedication;6
6;Acknowledgments;12
7;Preface;14
8;List of Tables;16
9;List of Figures;20
10;Chapter 1.
Introduction;22
10.1;1.1 Introductory Remarks;22
10.2;1.2 The Role of Order Statistics in Practical Applications;23
10.3;1.3 Scope of This Volume;25
11;Chapter 2.
Basic Theory;28
11.1;2.1 Introduction;28
11.2;2.2 Joint Distribution of n Order Statistics;28
11.3;2.3 Joint Distribution of Two Order Statistics;29
11.4;2.4 Distribution of a Single Order Statistic;32
11.5;2.5 Distribution of Range and Some Other Statistics
;38
12;Chapter 3.
Moments and Other Expected Values;42
12.1;3.1 Introduction;42
12.2;3.2 Some Basic Formulas;43
12.3;3.3 Recurrence Relations and Identities;44
12.4;3.4 Results for the Uni form Distribution;51
12.5;3.5 Results for the Exponential Distribution;55
12.6;3.6 Results for the Logistic Distribution;59
12.7;3.7 Results for the Gamma Distribution;64
12.8;3.8 Results for the Weibull Distribution;68
12.9;3.9 Results for the Normal Distribution;72
12.10;3.10 Results for the Half Logistic Distribution;84
12.11;3.11 David and Johnson's Approximation;89
13;Chapter 4. Linear Estimation Based on Order Statistics;94
13.1;4.1 Preliminary Remarks;94
13.2;4.2 BLUE of the Scale Parameter;95
13.3;4.3 BLUE for the One-Parameter Exponential Distribution;97
13.4;4.4 BLUEs of the Location and Scale Parameters;101
13.5;4.5 BLUEs for the Two-Parameter Exponential Distribution;108
13.6;4.6 Gupta's Simplified Linear Estimators;115
13.7;4.7 Blom's Unbiased Nearly Best Linear Estimators;121
13.8;4.8 Downton's Linear Estimators with Polynomial Coefficients;130
13.9;4.9 Details of Other Related Work;140
14;Chapter 5.
Maximum Likelihood Estimation;142
14.1;5.1 Preliminary Remarks;142
14.2;5.2 The Weibull Distribution;143
14.3;5.3 The Lognormal Distribution;147
14.4;5.4 The Inverse Gaussian Distribution;152
14.5;5.5 The Gamma Distribution;156
14.6;5.6 The Rayleigh Distribution;160
14.7;5.7 The Exponential Distribution;165
14.8;5.8 Complete, Truncated, and Censored Samples from the Normal Distribution;167
15;Chapter 6.
Approximate Maximum Likelihood Estimation;182
15.1;6.1 Preliminary Remarks;182
15.2;6.2 Estimation for the Rayleigh Distribution;183
15.3;6.3 Estimation for the Normal Distribution;188
15.4;6.4 Estimation for the Logistic Distribution;198
15.5;6.5 Estimation for the Extreme Value Distribution;207
15.6;6.6 Estimation for the Type I Generalized Logistic Distribution;218
15.7;6.7 Estimation for the Half Logistic Distribution;229
16;Chapter 7. Optimal Linear Estimation Based on Selected Order Statistics;236
16.1;7.1 Introduction;236
16.2;7.2 Bennett's and Jung's Optimal Asymptotic Estimators;237
16.3;7.3 Ogawa's Optimal Estimators Based on Selected Order Statistics;254
16.4;7.4 Dixon's Simplified Linear Estimators;270
16.5;7.5 Balakrishnan's Approximate Maximum Likelihood Estimation;276
16.6;7.6 Estimation of Population Quantiles;285
16.7;7.7 Details of Other Related Work;291
17;Chapter 8. Cohen–Whitten Estimators: Using Order Statistics;294
17.1;8.1 Preliminary Remarks;294
17.2;8.2 The Weibull Distribution;295
17.3;8.3 The Lognormal Distribution;299
17.4;8.4 The Inverse Gaussian Distribution;302
17.5;8.5 The Gamma Distribution;307
17.6;8.6 The Exponential Distribution;310
17.7;8.7 Illustrative Examples;311
18;Chapter 9. Estimation in Regression Models;320
18.1;9.1 Introduction;320
18.2;9.2 Best Linear Unbiased Estimation with Multiple Measurements;321
18.3;9.3 Modified Maximum Likelihood Estimation with Multiple Measurements;331
18.4;9.4 Modified Maximum Likelihood Estimation with Single Measurements;336
19;Chapter 10. A Sample Completion Technique for Censored Samples;350
19.1;10.1 Introductory Remarks;350
19.2;10.2 Censored Samples from the Normal Distribution;351
19.3;10.3 Censored Samples from Skewed Distributions;352
19.4;10.4 Illustrative Examples;356
20;Bibliography;362
21;Author Index;388
22;Subject Index;394