Bayesian Estimation and Prediction for a Hybrid Censored Lognormal Distribution

For a lognormal distribution, in Bayesian framework, we consider estimation of unknown parameters and prediction of future observable when it is known that samples are hybrid censored. We derive Bayes estimates with respect to the squared error loss function under both informative and non-informative prior situations. These estimates are then computed using Lindley method, importance sampling, and OpenBUGS software. For comparison purposes, we also obtain maximum-likelihood estimates using expectation-maximization (EM) algorithm, and compute Fisher information matrix as well. Predictive estimates of future observable are obtained under the setup of one- and two-sample prediction problems. We further compute equal-tail and highest posterior density predictive intervals, the corresponding average interval length and coverage percentage. Proposed methods of estimation and prediction are compared numerically, and comments are made based on a simulation study. Two real data sets are also analyzed for illustration purposes.