E-Bayesian Estimations of Reliability and Hazard Rate based on Generalized Inverted Exponential Distribution and Type II Censoring

Introduction      This paper is concerned with using the Maximum Likelihood, Bayes and a new method, E-Bayesian, estimations for computing estimates for the unknown parameter, reliability and hazard rate functions of the Generalized Inverted Exponential distribution. The estimates are derived based on a conjugate prior for the unknown parameter. E-Bayesian estimations are obtained based on three different prior distributions of the hyper parameters. Asymptotic behaviors of E-Bayesian estimations and relations among them have been discussed. The results are computed based on type-II censoring and squared error loss function. Finally, a comparison among the Maximum Likelihood, Bayes and E-Bayesian estimation methods in different sample sizes are made, using the Monte Carlo simulation, which shows that the new method is more efficient than other old methods and is easy to operate. Method    Suppose the Generalized Inverted Exponential distribution and its unknown parameter, reliability and hazard rate functions. Then the estimates of functions of interest are derived based on type II censored samples of this distribution, using the Monte Carlo simulation.  Results     Results show that the E-Bayesian method is more efficient than other old methods and is easy to operate. Also, the asymptotic behaviors of three E-Bayesian estimations are the same.