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.
Author(s): Jayant V. Deshpande, Sudha G Purohit
Year: 2006
Language: English
Pages: 258
Tags: Математика;Теория вероятностей и математическая статистика;Математическая статистика;Прикладная математическая статистика;Анализ выживаемости;
Contents ......Page 8
Preface ......Page 6
1. Introduction ......Page 11
2.1 Functions Characterizing Life-time Random Variable ......Page 23
2.2 Exponential Distribution as the Model for the No-Ageing ......Page 25
2.3 Positive Ageing ......Page 28
2.4 Negative Ageing ......Page 33
2.5 Relative Ageing of Two Probability Distributions ......Page 34
2.6 Bathtub Failure Rate ......Page 35
2.7 System Life-time ......Page 37
2.8 IFRA Closure Property ......Page 42
2.9 Bounds on the Reliability Function of an IFRA Distribution ......Page 43
3.2 Weibull Family ......Page 47
3.3 Gamma Family ......Page 49
3.4 Log-normal Family ......Page 50
3.5 Linear Failure Rate Family ......Page 52
3.7 Pareto Family ......Page 53
3.8 The Distribution of a Specific Parallel System ......Page 54
3.9 Lehmann Families ......Page 55
3.10 Choice of the Model ......Page 56
3.11 Some Further Properties of the Exponential Distribution ......Page 57
4.2 Method of Maximum Likelihood ......Page 61
4.3 Parameteric Analysis for Complete Data ......Page 66
4.4 Parametric Analysis of Censored Data ......Page 78
5.2 Uncensored (complete) Data ......Page 109
5.3 Censored Data ......Page 112
6.1 Introduction ......Page 139
6.2 U-Statistics ......Page 140
6.3 Tests For Exponentiality ......Page 145
7.1 Introduction ......Page 167
7.2 Complete or Uncensored Data ......Page 168
7.3 Randomly Censored (right) Data ......Page 170
8.1 Introduction ......Page 185
8.2 Complete Data ......Page 187
8.3 Censored Data ......Page 191
8.4 Test for Constant of Proportionality in PH Model ......Page 199
9.1 Introduction ......Page 211
9.2 The Model for General Competing Risks ......Page 212
9.3 Independent Competing Risks ......Page 213
9.5 The Likelihood for Parametric Models with Independent Latent Lifetimes ......Page 215
9.6 Tests for Stochastic Dominance of Independent Competing Risks ......Page 216
9.7 Tests for Proportionality of Hazard Rates of Independent Competing Risks ......Page 220
9.8 Tests in the Context of Dependent Competing Risks ......Page 222
10.1 Introduction ......Page 225
10.3 Probabilistic Models ......Page 226
10.4 Joint Distributions of the Failure Times ......Page 227
10.5 Estimation of Parameters ......Page 229
10.6 Unconditional Tests for the Time Truncated Case ......Page 231
Appendix A Statistical Analyses using R ......Page 237
References ......Page 249
Index ......Page 255
