Beyesian Statistical Inference on Mean Residual Life Function

Abstract

The mean residual function is very important in survival analysis, where lifetime distributions that model the time to a particular event are studied. This includes machine failure times, service and repair times, and event duration times, in general. The mean residual function provides the expected remaining life of lifetime distributions given that the distribution has survived up to a certain time. This function has important application in many fildes such as reliability, medical, and actuarial fildes. It can be used to characterize distribution through the inversion formula. Therfore, it can be used in fitting a model to the data. In this thesis, we investigate the main properties of the mean residual functions and express it in terms of mathematical formulas for some lifetime distributions. Then we use the Bayesian approach to performe statistical inference on the mean residual life function. To do so, we use some common Markov Chain Mont Carlo methods for the simulation. We also study Beyesiasn nonparametric inference for mean residual life functions obtained from a flexible mixture model for the corresponding survival distribution. In particular, we develop Markov Chain Monte Carlo posterior simulation methods to fit anonparametric gamma Dirichelet process mixture model to two experimental groups. To illustrate the practical utility of the nonparametric mixture model, we compare with an exponentiated Weibull model, aparametric survival distribution that allows various shapes for the mean residual life function.