Classical and Bayes Estimators for Exponential Distribution With Comparison of Different Priors & the El-Sayyad's loss function

Abstract

In this study, different estimators were used for estimating scale parameter for Exponential distribution, such as maximum likelihood estimator, moment estimator and the Bayes estimator, in six types when the prior distribution for the scale parameter is: Levy distribution, Gumbel type-II distribution, Inverse Chi-square distribution, Inverted Gamma distribution, improper distribution, Non-informative distribution. Under El-Sayyad's loss function .we used simulation technique, to compare the performance for each estimator, several cases from Exponential distribution for data generating, for different sample sizes (small, medium, and large). Simulation results shown that The best method is the bayes estimation ,when the prior distribution for is improper distribution with (a=9, b=1) and for the values for the parameters of the El-Sayyad 's loss function is ( ),when the true value of ( ).And the non-informative distribution with ( c=8) and for the values for the parameters of the El-Sayyad 's loss function is ( ), when the true value of ( ).Also the non-informative distribution with ( c=8) and for the values for the parameters of the El-Sayyad 's loss function is ( ),when the true value of ( ), according to the smallest values of MSE for all samples sizes (n) comparative to the estimated values by using Maximum likelihood estimation method (MLE) and Moment estimation method (ME).