Analysis of Interval-Censored Data with Weibull Lifetime Distribution

Abstract

In this work the analysis of interval-censored data, with Weibull distribution as the underlying lifetime distribution has been considered. It is assumed that censoring mechanism is independent and non-informative. As expected, the maximum likelihood estimators cannot be obtained in closed form. In our simulation experiments it is observed that the Newton-Raphson method may not converge many times. An expectation maximization algorithm has been suggested to compute the maximum likelihood estimators, and it converges almost all the times. The Bayes estimates of the unknown parameters under gamma priors are considered. If the shape parameter is known, the Bayes estimate of the scale parameter can be obtained in explicit form. When both the parameters are unknown, the Bayes estimators cannot be obtained in explicit form. Lindley’s approximation, importance sampling procedures and Metropolis Hastings algorithm are used to compute the Bayes estimates. Highest posterior density credible intervals of the unknown parameter are obtained using importance sampling technique. Small simulation experiments are conducted to investigate the finite sample performance of the proposed estimators, and the analysis of two data sets; one simulated and one real life, have been provided for illustrative purposes.