AN EXTENDED STUDY TO DETERMINE THE BEST LOSS FUNCTIONS FOR ESTIMATING THE EXPONENTIAL DISTRIBUTION PARAMETER UNDERN EXTENDED STUDY TO DETERMINE THE BEST LOSS FUNCTIONS FOR ESTIMATING THE EXPONENTIAL DISTRIBUTION PARAMETER UNDER JEFFERY AND GAMMA PRIORS

Abstract

In this research, we compared the Bayesian estimators when estimating the scale parameter for the exponential distribution by using different loss functions under Jeffrey and Gamma priors, as most of the available symmetric and asymmetric loss functions were used, also the balanced and unbalanced loss functions. The simulation results proved the advantage of balanced loss functions with the Gamma prior, and the effectiveness of the balanced loss functions when using Jeffrey prior especially if the value of the weighted coefficient is equal to 0.5, so it is possible to use initial estimators as maximum likelihood estimator to compensate for the lack of prior information around the parameter to be estimated, also the advantage of the balanced general entropy loss function and the balanced weighted square error loss function under Jeffrey prior when the value of the scale parameter for the exponential distribution is less than 1, the preference of the balanced weighted square error loss function and the balanced K loss function if the value of the scale parameter for the exponential distribution is equal to 1, and the preference for the AL-Sayyad balanced loss function and the balanced AL-Bayyati loss function if the value of the scale parameter for the exponential distribution is greater or equal to 2.