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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.
Front Cover; Order Statistics and Inference:Estimation Methods; Copyright Page; Dedication; Table of Contents; Acknowledgments; Preface; List of Tables; List of Figures; Chapter 1. Introduction; 1.1 Introductory Remarks; 1.2 The Role of Order Statistics in Practical Applications; 1.3 Scope of This Volume; Chapter 2. Basic Theory; 2.1 Introduction; 2.2 Joint Distribution of n Order Statistics; 2.3 Joint Distribution of Two Order Statistics; 2.4 Distribution of a Single Order Statistic; 2.5 Distribution of Range and Some Other Statistics; Chapter 3. Moments and Other Expected Values
3.1 Introduction3.2 Some Basic Formulas; 3.3 Recurrence Relations and Identities; 3.4 Results for the Uni form Distribution; 3.5 Results for the Exponential Distribution; 3.6 Results for the Logistic Distribution; 3.7 Results for the Gamma Distribution; 3.8 Results for the Weibull Distribution; 3.9 Results for the Normal Distribution; 3.10 Results for the Half Logistic Distribution; 3.11 David and Johnson's Approximation; Chapter 4. Linear Estimation Based on Order Statistics; 4.1 Preliminary Remarks; 4.2 BLUE of the Scale Parameter; 4.3 BLUE for the One-Parameter Exponential Distribution
4.4 BLUEs of the Location and Scale Parameters4.5 BLUEs for the Two-Parameter Exponential Distribution; 4.6 Gupta's Simplified Linear Estimators; 4.7 Blom's Unbiased Nearly Best Linear Estimators; 4.8 Downton's Linear Estimators with Polynomial Coefficients; 4.9 Details of Other Related Work; Chapter 5. Maximum Likelihood Estimation; 5.1 Preliminary Remarks; 5.2 The Weibull Distribution; 5.3 The Lognormal Distribution; 5.4 The Inverse Gaussian Distribution; 5.5 The Gamma Distribution; 5.6 The Rayleigh Distribution; 5.7 The Exponential Distribution
5.8 Complete, Truncated, and Censored Samples from the Normal DistributionChapter 6. Approximate Maximum Likelihood Estimation; 6.1 Preliminary Remarks; 6.2 Estimation for the Rayleigh Distribution; 6.3 Estimation for the Normal Distribution; 6.4 Estimation for the Logistic Distribution; 6.5 Estimation for the Extreme Value Distribution; 6.6 Estimation for the Type I Generalized Logistic Distribution; 6.7 Estimation for the Half Logistic Distribution; Chapter 7. Optimal Linear Estimation Based on Selected Order Statistics; 7.1 Introduction
7.2 Bennett's and Jung's Optimal Asymptotic Estimators7.3 Ogawa's Optimal Estimators Based on Selected Order Statistics; 7.4 Dixon's Simplified Linear Estimators; 7.5 Balakrishnan's Approximate Maximum Likelihood Estimation; 7.6 Estimation of Population Quantiles; 7.7 Details of Other Related Work; Chapter 8. Cohen-Whitten Estimators: Using Order Statistics; 8.1 Preliminary Remarks; 8.2 The Weibull Distribution; 8.3 The Lognormal Distribution; 8.4 The Inverse Gaussian Distribution; 8.5 The Gamma Distribution; 8.6 The Exponential Distribution; 8.7 Illustrative Examples
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Includes bibliographical references (pages 341-366) and indexes.
Statistical modeling and decision science