Balakrishnan / Cohen Order Statistics & Inference

Estimation Methods
1. Auflage 2014
ISBN: 978-1-4832-9749-1
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 392 Seiten, Web PDF

The literature on order statistics and inferenc eis quite extensive and covers a large number of fields ,but most of it is dispersed throughout numerous publications. This volume is the consolidtion of the most important results and places an emphasis on estimation. Both theoretical and computational procedures are presented to meet the needs of researchers, professionals, and students. The methods of estimation discussed are well-illustrated with numerous practical examples from both the physical and life sciences, including sociology,psychology,a nd electrical and chemical engineering. A complete, comprehensive bibliography is included so the book can be used both aas a text and reference.

Narayanaswamy Balakrishnan is a distinguished university professor in the Department of Mathematics and Statistics at McMaster University Hamilton, Ontario, Canada. He is an internationally recognized expert on statistical distribution theory, and a book-powerhouse with over 24 authored books, four authored handbooks, and 30 edited books under his name. He is currently the Editor-in-Chief of Communications in Statistics published by Taylor & Francis. He was also the Editor-in-Chief for the revised version of Encyclopedia of Statistical Sciences published by John Wiley & Sons. He is a Fellow of the American Statistical Association and a Fellow of the Institute of Mathematical Statistics. In 2016, he was awarded an Honorary Doctorate from The National and Kapodistrian University of Athens, Athens, Greece. In 2021, he was elected as a Fellow of the Royal Society of Canada.

Autoren/Hrsg.

Balakrishnan, Narayanaswamy

Cohen, A. Clifford

Inhaltsverzeichnis

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