Nonparametric Statistical Methods, 3rd Edition

Chapter 11

Life Distributions and Survival Analysis

Introduction

In Sections 11.1–11.4 we consider a sample of lifelengths from an underlying life distribution (i.e., a distribution that puts all of its probability on nonnegative values). There are many nonparametric classes of life distributions that are used to describe aging. We focus on six natural classes that have easily understood physical interpretations. The classes are the increasing failure rate (IFR) class, the increasing failure rate average (IFRA) class, the new better than used (NBU) class, the new better than used in expectation (NBUE) class, the decreasing mean residual life (DMRL) class, and the initially increasing then decreasing mean residual life (IDMRL) class. In Sections 11.1–11.4 we describe tests of the null hypothesis of exponentiality. Section 11.1 considers IFR and IFRA alternatives. Section 11.2 considers NBU and NBUE alternatives. Section 11.3 considers DMRL alternatives and also presents confidence bands for the mean residual life function. Section 11.4 considers IDMRL alternatives, and the tests presented are designed to detect a trend change in the mean residual life. Section 11.5 presents a nonparametric confidence band for the distribution function. Sections 11.6 and 11.7 are devoted to censored data. Section 11.6 contains, for censored data, an estimator of the distribution function, confidence bands for the distribution function, and confidence bands for the quantile function. Section 11.7 ...