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E-raamat: Lifetime Data: Statistical Models And Methods (Second Edition)

(Univ Of Pune, India), (Univ Of Pune, India)
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This book is meant for postgraduate modules that cover lifetime data in reliability and survival analysis as taught in statistics, engineering statistics and medical statistics courses. It is helpful for researchers who wish to choose appropriate models and methods for analyzing lifetime data. There is an extensive discussion on the concept and role of ageing in choosing appropriate models for lifetime data, with a special emphasis on tests of exponentiality. There are interesting contributions related to the topics of ageing, tests for exponentiality, competing risks and repairable systems. A special feature of this book is that it introduces the public domain R-software and explains how it can be used in computations of methods discussed in the book.This new edition includes new sections on Frailty Models and Accelerated Life Time Models. Many more illustrations and exercises are also included.
1 Introduction
1(12)
2 Ageing
13(24)
2.1 Introduction
13(1)
2.2 Functions Characterising Lifetime Random Variable
13(2)
2.3 Exponential Distribution as Model for No-Ageing
15(3)
2.4 Positive Ageing
18(5)
2.5 Negative Ageing
23(1)
2.6 Relative Ageing of Two Probability Distributions
23(1)
2.7 Bathtub Failure Rate
24(3)
2.8 System Lifetime
27(4)
2.9 IFRA Closure Property
31(2)
2.10 Bounds on the Reliability Function of an IFRA Distribution
33(4)
3 Some Parametric Families of Probability Distributions
37(16)
3.1 Introduction
37(1)
3.2 Weibull Family
37(2)
3.3 Gamma Family
39(1)
3.4 Log-Normal Family
40(3)
3.5 Linear Failure Rate Family
43(1)
3.6 Makeham Family
43(1)
3.7 Pareto Family
43(1)
3.8 The Distribution of a Specific Parallel System
44(2)
3.9 Lehmann Families
46(1)
3.10 Choice of the Model
46(1)
3.11 Some Further Properties of the Exponential Distribution
47(6)
4 Parametric Analysis of Survival Data
53(54)
4.1 Introduction
53(1)
4.2 Method of Maximum Likelihood
53(5)
4.3 Parametric Analysis for Complete Data
58(12)
4.4 Parametric Analysis of Censored Data
70(37)
5 Non-parametric Estimation of the Survival Function
107(34)
5.1 Introduction
107(1)
5.2 Uncensored (complete) Data
107(3)
5.3 Censored Data
110(31)
6 Tests for Exponentiality
141(30)
6.1 Introduction
141(1)
6.2 U-Statistics
141(5)
6.3 Tests for Exponentiality
146(25)
7 Two-sample Non-parametric Problem
171(20)
7.1 Introduction
171(1)
7.2 Complete or Uncensored Data
172(2)
7.3 Randomly Censored (right) Data
174(17)
8 Proportional Hazards and Other Regression Models
191(50)
8.1 Introduction
191(2)
8.2 Complete Data
193(4)
8.3 Censored Data
197(8)
8.4 Test for Constant of Proportionality in PH Model
205(7)
8.5 Frailty Model
212(7)
8.6 Accelerated Lifetime (ALT) Model
219(22)
9 Analysis of Competing Risks
241(18)
9.1 Introduction
241(1)
9.2 The Model for General Competing Risks
242(1)
9.3 Independent Competing Risks
243(2)
9.4 Bounds on the Joint Survival Function
245(1)
9.5 The Likelihood for Parametric Models with Independent Latent Lifetimes
245(1)
9.6 Tests for Stochastic Dominance of Independent Competing Risks
246(4)
9.7 Tests for Proportionality of Hazard Rates of Independent Competing Risks
250(3)
9.8 Tests in the Context of Dependent Competing Risks
253(6)
10 Repairable Systems
259(12)
10.1 Introduction
259(1)
10.2 Repair Models
260(1)
10.3 Probabilistic Models
260(1)
10.4 Joint Distributions of the Failure Times
261(2)
10.5 Estimation of Parameters
263(2)
10.6 Unconditional Tests for the Time Truncated Case
265(6)
Appendix: Statistical Analyses Using R 271(12)
References 283(8)
Index 291
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