Author	Balakrishnan, N. author
Title	Progressive Censoring [electronic resource] : Theory, Methods, and Applications / by N. Balakrishnan, Rita Aggarwala
Imprint	Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 2000
Connect to	http://dx.doi.org/10.1007/978-1-4612-1334-5
Descript	XV, 248 p. online resource

Censored sampling arises in a life-testing experiment whenever the experimenter does not observe (either intentionally or unintentionally) the failure times of all units placed on a life-test. Inference based on censored sampling has been studied during the past 50 years by numerous authors for a wide range of lifetime distributions such as normal, exponential, gamma, Rayleigh, Weibull, extreme value, log-normal, inverse Gaussian, logistic, Laplace, and Pareto. Naturally, there are many different forms of censoring that have been discussed in the literature. In this book, we consider a versatile scheme of censoring called progressive Type-II censoring. Under this scheme of censoring, from a total of n units placed on a life-test, only m are completely observed until failure. At the time of the first failure, Rl of the n - 1 surviving units are randomly withdrawn (or censored) from the life-testing experiment. At the time of the next failure, R2 of the n - 2 -Rl surviving units are censored, and so on. Finally, at the time of the m-th failure, all the remaining Rm = n - m -Rl - . . . - Rm-l surviving units are censored. Note that censoring takes place here progressively in m stages. Clearly, this scheme includes as special cases the complete sample situation (when m = nand Rl = . . . = Rm = 0) and the conventional Type-II right censoring situation (when Rl = . . . = Rm-l = 0 and Rm = n - m)

1 Introduction -- 1.1 The Big Picture -- 1.2 Genesis -- 1.3 The Need for Progressive Censoring -- 1.4 A Relatively Unexplored Idea -- 1.5 Mathematical Notations -- 1.6 A Friendly Note -- 2 Mathematical Properties of Progressively Type-II Right Censored Order Statistics -- 2.1 General Continuous Distributions -- 2.2 The Exponential Distribution: Spacings -- 2.3 The Uniform Distribution: Ratios -- 2.4 The Pareto Distribution: Ratios -- 2.5 Bounds for Means and Variances -- 3 Simulational Algorithms -- 3.1 Introduction -- 3.2 Simulation Using the Uniform Distribution -- 3.3 Simulation Using the Exponential Distribution -- 3.4 General Progressively Type-II Censored Samples -- 4 Recursive Computation and Algorithms -- 4.1 Introduction -- 4.2 The Exponential Distribution -- 4.3 The Doubly Truncated Exponential Distribution -- 4.4 The Pareto Distribution and Truncated Forms -- 4.5 The Power Function Distribution and Truncated Forms -- 5 Alternative Computational Methods -- 5.1 Introduction -- 5.2 Formulas in Terms of Moments of Usual Order Statistics -- 5.3 Formulas in the Case of Symmetric Distributions -- 5.4 Other Relations for Moments -- 5.5 First-Order Approximations to the Moments -- 6 Linear Inference -- 6.1 One-Parameter (Scale) Models -- 6.2 Two-Parameter (Location-Scale) Models -- 6.3 Best Linear Invariant Estimation -- 7 Likelihood Inference: Type-I and Type-II Censoring -- 71. Introduction -- 7.2 General Continuous Distributions -- 7.3 Specific Continuous Distributions -- 8 Linear Prediction -- 8.1 Introduction -- 8.2 The Exponential Case -- 8.3 Case of General Distributions -- 8.4 A Simple Approach Based on BLUEs -- 8.5 First-Order Approximations to BLUPs -- 8.6 Prediction Intervals -- 8.7 Illustrative Examples -- 9 Conditional Inference -- 9.1 Introduction -- 9.2 Inference for Location and Scale Parameters -- 9.3 Inference for Quantiles and Reliability and Prediction Intervals -- 9.4 Results for Extreme Value Distribution -- 9.5 Results for Exponential Distribution -- 9.6 Illustrative Examples -- 9.7 Results for Pareto Distribution -- 10 Optimal Censoring Schemes -- 10.1 Introduction -- 10.2 The Exponential Distribution -- 10.3 The Normal Distribution -- 10.4 The Extreme Value Distribution -- 10.5 The Extreme Value (II) Distribution -- 10.6 The Log-Normal Distribution -- 10.7 Tables -- 11 Acceptance Sampling Plans -- 11.1 Introduction -- 11.2 The Exponential Distribution -- 11.3 The Log-Normal Distribution -- Author Index

1. Mathematics
2. Probabilities
3. Statistics
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