Exponential Distribution: Theory, Methods and Applications

✍ Scribed by Balakrishnan, K.; Basu, Asit P

• Publisher: Routledge;CRC
• Year: 2018
• Tongue: English
• Leaves: 665
• Category: Library

✦ Table of Contents

Content: Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
List of Tables
List of Figures
Preface
List of Contributors
1: Genesis
1.1 Preliminaries
1.2 Historical Remarks
References
2: Basic Distributional Results and Properties
2.1 Introduction
2.2 Basic Results and Properties
References
3: Order Statistics and Their Properties
3.1 Introduction
3.2 Basic Distributional Results and Properties
3.3 Recurrence Relations
3.4 Lorenz Ordering
3.5 Asymptotic Distributions
3.6 Relationship to Uniform Order Statistics
3.7 Relationship to Geometric Order Statistics 3.8 Relationship to Double Exponential Order Statistics3.9 Results for a Progressive Type-II Censored Sample
3.10 Results for Right-Truncated Exponential Distribution
3.11 Results for Doubly-Truncated Exponential Distribution
References
4: MLEs Under Censoring and Truncation and Inference
4.1 Introduction
4.2 Parameter Estimation from Censored Samples
4.3 Estimation in Truncated Distributions
4.4 Errors of Estimates
4.5 Illustrative Examples
References
5: Linear Estimation Under Censoring and Inference
5.1 Introduction
5.2 Type-II Right Censored Samples 5.3 Type-II Doubly Censored Samples5.4 Type-II Multiply Censored Samples
5.5 Type-II Progressively Right Censored Samples
5.6 General Type-II Progressively Censored Samples
5.7 Asymptotic Best Linear Unbiased Estimation Based On Optimally Selected Order Statistics
5.8 Illustrative Examples
References
6: Reliability Estimation and Applications
6.1 Introduction
6.2 Estimation with the One-Parameter Model
6.3 Estimation with the Two-Parameter Model
References
7: Inferences Under Two-Sample and Multi-Sample Situations
7.1 Introduction
7.2 Notation and Preliminaries 7.3 Two-Sample Inferences Under Independent Type II Censoring7.4 Comparison of Several Populations Under Independent Type II Censoring
7.5 Two-Sample Inferences Under Joint Type II Censoring
7.6 Miscellaneous Other Results
References
8: Tolerance Limits and Acceptance Sampling Plans
8.1 Introduction
8.2 One-Sided Tolerance Limits
8.3 One- and Two-Sided Sampling Plans
8.4 Bayesian Sampling Plans
References
9: Prediction Problems
9.1 Introduction
9.2 Types of Prediction Problems
9.3 Best Linear Unbiased and Invariant Predictors
9.4 Maximum Likelihood Prediction 9.5 Prediction Intervals and Regions9.6 Bayes Predictors and Prediction Regions
9.7 Other Prediction Methods
9.8 Miscellaneous Results
9.9 Concluding Remarks
References
10: Bayesian Inference and Applications
10.1 Introduction
10.2 Bayesian Concepts
10.3 Life Testing and Reliability Estimation
10.4 Bayesian Classification Rules
References
11: Conditional Inference and Applications
11.1 Ancillarity and Conditionality: A Brief Overview
11.2 A Simple Example
11.3 One-Parameter Exponential Model
11.4 Exponential Regression
11.5 Discussion
References
12: Characterizations