Some Bayes' Estimators for Laplace Distribution under Different Loss Functions

The object of the present paper is to compare maximum likelihood estimator and some Bayes' estimators for the scale parameter of Laplace distribution. Two prior information functions are considered; the extension of Jeffreys prior and a new suggested prior which we call the modified inverse gamma prior. Two loss functions were considered: the squared and the modified squared error loss functions. We explore the performance of these estimators numerically under different conditions. The comparison was based on a Monte Carlo simulation study. The efficiency for the estimators was compared according to the mean square error (MSE) and the mean percentage error (MPE). The results of comparison by MSE and MPE showed that the Bayes' estimator of the scale parameter with the modified inverse gamma prior was the best particularly when �� is large. The maximum likelihood estimator was the second best estimator. While comparison with respect to loss functions showed that Bayes' estimators under modified squared error loss function gives better results than the squared error loss function.