On E-Bayesian estimations for the cumulative hazard rate and mean residual life under generalized inverted exponential distribution and type-II censoring.

Estimation of reliability and hazard rate is necessary in many applications. To this aim, different methods of estimation have been employed. Each method suffers from its own problems such as complexity of calculations, high risk and so on. Toward this end, this study employed a new method, E-Bayesian, for estimating the parametric functions of the Generalized Inverted Exponential distribution, which is one of the most noticeable distributions in lifetime studies. Relations are derived under a squared error loss function, type-II censoring and a conjugate prior. E-Bayesian estimations are obtained based on different priors of the hyperparameters to investigate the influence of different prior distributions on these estimations. The asymptotic behaviors of E-Bayesian estimations and relations among them have been investigated. Finally, a comparison among the maximum likelihood, Bayes and E-Bayesian estimations in different sample sizes are made, using a real data and the Monte Carlo simulation. Simulations show that the new presented method is more efficient than previous methods and is also easy to operate. Also, some comparisons among the results of Generalized Inverted Exponential distribution, Exponential distribution and Generalized Exponential distribution are provided.