Life-time Data: Statistical Models And Methods

by Hargreaves, Justin S. J.

• ISBN13: 9789812566072
• ISBN10: 9812566074
• Format: Hardcover
• Copyright: 2006-04-11
• 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	p. v
Introduction	p. 1
Ageing	p. 13
Functions Characterizing Life-time Random Variable	p. 13
Exponential Distribution as the Model for the No-ageing	p. 15
Positive Ageing	p. 18
Negative Ageing	p. 23
Relative Ageing of Two Probability Distributions	p. 24
Bathtub Failure Rate	p. 25
System Life-time	p. 27
IFRA Closure Property	p. 32
Bounds on the Reliability Function of an IFRA Distribution	p. 33
Some Parametric Families of Probability Distributions	p. 37
Introduction	p. 37
Weibull Family	p. 37
Gamma Family	p. 39
Log-normal Family	p. 40
Linear Failure Rate Family	p. 42
Makeham Family	p. 43
Pareto Family	p. 43
The Distribution of a Specific Parallel System	p. 44
Lehmann Families	p. 45
Choice of the Model	p. 46
Some Further Properties of the Exponential Distribution	p. 47
Parametric Analysis of Survival Data	p. 51
Introduction	p. 51
Method of Maximum Likelihood	p. 51
Parameteric Analysis for Complete Data	p. 56
Parametric Analysis of Censored Data	p. 68
Nonparametric Estimation of the Survival Function	p. 99
Introduction	p. 99
Uncensored (complete) Data	p. 99
Censored Data	p. 102
Tests for Exponentiality	p. 129
Introduction	p. 129
U-Statistics	p. 130
Tests For Exponentiality	p. 135
Two Sample Non-parametric Problem	p. 157
Introduction	p. 157
Complete or Uncensored Data	p. 158
Randomly Censored (right) Data	p. 160
Proportional Hazards Model: A Method of Regression	p. 175
Introduction	p. 175
Complete Data	p. 177
Censored Data	p. 181
Test for Constant of Proportionality in PH Model	p. 189
Analysis of Competing Risks	p. 201
Introduction	p. 201
The Model for General Competing Risks	p. 202
Independent Competing Risks	p. 203
Bounds on the Joint Survival Function	p. 205
The Likelihood for Parametric Models with Independent Latent Lifetimes	p. 205
Tests for Stochastic Dominance of Independent Competing Risks	p. 206
Tests for Proportionality of Hazard Rates of Independent Competing Risks	p. 210
Tests in the Context of Dependent Competing Risks	p. 212
Repairable Systems	p. 215
Introduction	p. 215
Repair Models	p. 216
Probabilistic Models	p. 216
Joint Distributions of the Failure Times	p. 217
Estimation of Parameters	p. 219
Unconditional Tests for the Time Truncated Case	p. 221
Statistical Analyses using R	p. 227
References	p. 239
Index	p. 245
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