Order Statistics and Inference : Estimation Methods.

Front Cover -- Order Statistics and Inference: Estimation Methods -- Copyright Page -- Table of Contents -- Dedication -- 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 Introduction -- 3.2 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 Parameters -- 4.5 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 Distribution -- Chapter 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 Estimators -- 7.3 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 -- Chapter 9. Estimation in Regression Models -- 9.1 Introduction -- 9.2 Best Linear Unbiased Estimation with Multiple Measurements -- 9.3 Modified Maximum Likelihood Estimation with Multiple Measurements -- 9.4 Modified Maximum Likelihood Estimation with Single Measurements -- Chapter 10. A Sample Completion Technique for Censored Samples -- 10.1 Introductory Remarks -- 10.2 Censored Samples from the Normal Distribution -- 10.3 Censored Samples from Skewed Distributions -- 10.4 Illustrative Examples -- Bibliography -- Author Index -- Subject Index.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.