Analysis of middle-censored data with exponential lifetime distributions

Recently Jammalamadaka and Mangalam [2003. Non-parametric estimation for middle censored data. J. Nonparametric Statist. 15, 253–265] introduced a general censoring scheme called the “middle-censoring” scheme in non-parametric set up. In this paper we consider this middle-censoring scheme when the lifetime distribution of the items is exponentially distributed and the censoring mechanism is independent and non-informative. In this set up, we derive the maximum likelihood estimator and study its consistency and asymptotic normality properties. We also derive the Bayes estimate of the exponential parameter under a gamma prior. Since a theoretical construction of the credible interval becomes quite difficult, we propose and implement Gibbs sampling technique to construct the credible intervals. Monte Carlo simulations are performed to evaluate the small sample behavior of the techniques proposed. A real data set is analyzed to illustrate the practical application of the proposed methods.