e-bayesian estimation

In this paper‎, ‎Bayesian and expected Bayesian (E-Bayesian) estimation of premium with exponential claim size is considered‎. ‎After calculation of premium using Heilmann principal‎, ‎its Bayesian and E-Bayesian estimation under three priors of hyper-parameters are obtained‎. ‎Then‎, ‎formulas for E-MSE are provided‎. ‎A Monte Carlo simulation is conducted for comparison of E-Bayesian estimators of premium‎. ‎A real example is presented for illustration of the results‎.

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.

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.

Sometimes the extent of the parameter domain changes over the space of the parameter, increases the risk of posterior Bayesian. In this case, the empirical and hierarchical estimates can be a good substitute for bayesian estimation. In this study, when X and Y are two independent exponential distributions with different parameters, were estimated the E-Bayesian and hierarchical Bayesian for the under squared error loss function. This suggested methods, was compared with each other and with the Bayesian estimator using the Monte Carlo simulation and two set data.