Reliability estimation and prediction for extension of exponential distribution using informative and non-informative priors

Abstract

In this article, we consider the classical and Bayesian estimation of the parameters and reliability characteristics of extension of exponential distribution. Classical estimation has been concerned through maximum likelihood estimation. Bayesian estimation procedure is carried out under the assumption that parameters having independent gamma priors using squared error loss function for complete sample. It is well known, in the two parameter family of distributions the Bayes estimates may not obtained in explicit form. Therefore, for simplicity here we use Lindley’s approximation to compute Bayes estimates. But, through this approximation technique it is not possible to compute the interval estimates of the parameters. Therefore, we also propose Gibbs sampling method to generate sample from the posterior distribution. On the basis of generated posterior sample we computed the Bayes estimates of the unknown parameters and constructed 95 % highest posterior density credible intervals. A Monte Carlo simulation study is carried out to compare the performance of Bayes estimators with the corresponding classical estimators in terms of their simulated risk. A real data set has been considered for illustrative purpose of the study. Furthermore, we have discussed about the Bayesian prediction of future observation based on the observed sample.