The Hazard rate : Theory and inference (with supplementary MATLAB-Programs)

Abstract

The hazard rate or failure rate is a special measure of risk. It roughly gives the probability of quitting a givenstate after having spent a given time in that state, and as such it is very popular in the life sciences for lifetimeanalysis and in technology for reliability analysis and maintenance. Part I of the monograph is descriptive and devoted to probability aspects of the hazard rate. Chapter 1 shows how it is related to other functions describing stochastic lifetime in the continuous and discrete as well as inthe univariate and multivariate cases. Chapter 2 introduces and explores several classes of aging. Chapter 3,supplemented by plot-offering MATLAB-programs, gives among others the hazard rate and the meanresidual life function of more than 90 continuous and discrete statistical distributions. Part II is devoted to the inference of the hazard rate. After presenting sampling techniques for lifetime data in Chapter 4, point estimators are given in Chapter 5 for ungrouped data and in Chapter 6 for grouped date.Maximum likelihood estimators of monotone hazard rate are found in Chapter 7. The core of Part II is Chapter 8showing how to find smooth estimators, especially kernel estimators. Chapter 9 is on hazard plotting and Chapter 10gives a lot of tests on hypotheses concerning the hazard rate and on aging properties. A collection of MATLAB-programshelps in estimating and testing.