Life Time Data : Statistical Models and Methods

by Deshpande, Jayant V.; Purohit, Sudha G.

• ISBN13: 9789812566973
• ISBN10: 981256697X
• Format: Paperback
• Copyright: 2006-01-30
• Publisher: World Scientific Pub Co Inc

Summary

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. Contents: Ageing; Some Parametric Families of Probability Distributions; Parametric Analysis of Survival Data; Nonparametric Estimation of the Survival Function; Tests of Exponentiality; Two Sample Nonparametric Problems; Proportional Hazards Model: A Method of Regression; Analysis of Competing Risks; Repairable Systems. Key Features Special emphasis on ageing and tests of exponentiality and their role in choosing appropriate models for lifetime data Extensive discussion of classical parametric and nonparametric models and relevant inference Documentation of new results in ageing, testing for competing risks and repairable systems Readership: Graduate students, academics and researchers in probability and statistics, industrial engineering, decision sciences and bioinformatics.

Table of Contents

Preface	v
1. Introduction	1	(12)
2. Ageing	13	(24)
2.1 Functions Characterizing Life-time Random Variable	13	(2)
2.2 Exponential Distribution as the Model for the No-ageing	15	(3)
2.3 Positive Ageing	18	(5)
2.4 Negative Ageing	23	(1)
2.5 Relative Ageing of Two Probability Distributions	24	(1)
2.6 Bathtub Failure Rate	25	(2)
2.7 System Life-time	27	(5)
2.8 IFRA Closure Property	32	(1)
2.9 Bounds on the Reliability Function of an IFRA Distribution	33	(4)
3. Some Parametric Families of Probability Distributions	37	(14)
3.1 Introduction	37	(1)
3.2 Weibull Family	37	(2)
3.3 Gamma Family	39	(1)
3.4 Log-normal Family	40	(2)
3.5 Linear Failure Rate Family	42	(1)
3.6 Makeham Family	43	(1)
3.7 Pareto Family	43	(1)
3.8 The Distribution of a Specific Parallel System	44	(1)
3.9 Lehmann Families	45	(1)
3.10 Choice of the Model	46	(1)
3.11 Some Further Properties of the Exponential Distribution	47	(4)
4. Parametric Analysis of Survival Data	51	(48)
4.1 Introduction	51	(1)
4.2 Method of Maximum Likelihood	51	(5)
4.3 Parameteric Analysis for Complete Data	56	(12)
4.4 Parametric Analysis of Censored Data	68	(31)
5. Nonparametric Estimation of the Survival Function	99	(58)
5.1 Introduction	99	(1)
5.2 Uncensored (complete) Data	99	(3)
5.3 Censored Data	102	(27)
6. Tests for Exponentiality	129	(1)
6.1 Introduction	129	(1)
6.2 U-Statistics	130	(5)
6.3 Tests For Exponentiality	135	(22)
7. Two Sample Non-parametric Problem	157	(18)
7.1 Introduction	157	(1)
7.2 Complete or Uncensored Data	158	(2)
7.3 Randomly Censored (right) Data	160	(15)
8. Proportional Hazards Model: A Method of Regression	175	(26)
8.1 Introduction	175	(2)
8.2 Complete Data	177	(4)
8.3 Censored Data	181	(8)
8.4 Test for Constant of Proportionality in PH Model	189	(12)
9. Analysis of Competing Risks	201	(14)
9.1 Introdcution	201	(1)
9.2 The Model for General Competing Risks	202	(1)
9.3 Independent Competing Risks	203	(2)
9.4 Bounds on the Joint Survival Function	205	(1)
9.5 The Likelihood for Parametric Models with Independent Latent Lifetimes	205	(1)
9.6 Tests for Stochastic Dominance of Independent Competing Risks	206	(4)
9.7 Tests for Proportionality of Hazard Rates of Independent Competing Risks	210	(2)
9.8 Tests in the Context of Dependent Competing Risks	212	(3)
10. Repairable Systems	215	(12)
10.1 Introduction	215	(1)
10.2 Repair Models	216	(1)
10.3 Probabilistic Models	216	(1)
10.4 Joint Distributions of the Failure Times	217	(2)
10.5 Estimation of Parameters	219	(2)
10.6 Unconditional Tests for the Time Truncated Case	221	(6)
Appendix A Statistical Analyses using R	227	(12)
References	239	(6)
Index	245