Estimation issues in the Exponential–Logarithmic model under hybrid censoring

Abstract

In this paper we develop both frequentist and Bayesian estimation methodologies for parameters of an Exponential–Logarithmic Distribution under Type-I hybrid censoring. In frequentist approach, it is observed that the Maximum Likelihood Estimators (MLEs) do not have closed form expressions. We use both the EM and SEM algorithms to compute the MLEs and using the missing information principle obtain the observed Fisher information matrix which is then used to construct the asymptotic confidence intervals. Further, two bootstrap interval estimates are proposed for the unknown parameters. Under squared error loss and LINEX loss functions, we obtain Bayes estimates of the unknown parameters assuming independent gamma and beta priors using the Lindley method, Tierney–Kadane method and the importance sampling procedure. The problem of prediction is also explored. A real life data set as well as simulated data have been analyzed for illustrative purposes.