Parameter estimation of Lindley distribution with hybrid censored data

This study deals with the classical and Bayesian analysis of the hybrid censored lifetime data under the assumption that the lifetime follow Lindley distribution. In classical set up, the maximum likelihood estimate of the parameter with its standard error are computed. Further, by assuming Jeffrey's invariant and gamma priors of the unknown parameter, Bayes estimate along with its posterior standard error and highest posterior density credible intervals of the parameter are obtained. Markov Chain Monte Carlo technique such as Metropolis-Hastings algorithm has been utilized to generate draws from the posterior density of the parameter. A real data set representing the waiting time of the bank customers has been analyzed for illustration purpose. A comparison study is conducted to judge the performance of the classical and Bayesian estimation procedure.