Bayesian and Non-Bayesian Estimation for the Scale Parameter of Laplace Distribution

In this paper we derived some Bayesian estimators of the scale parameter for the Laplace distribution under different loss function including the squared log error loss function, Quadratic loss function and Entropy loss function. Also some classical estimators have been obtained, such as Maximum likelihood Estimator, Uniformly Minimum Variance Unbiased Estimator and Minimum Mean Squared Error estimator. The estimators have been derived with considering two cases, one where the location parameter a, is known and constant and the other where the location parameter is unknown and estimated it by median which is the Maximum likelihood estimator for a. All estimators of the scale parameter are compared empirically through Monte Carlo simulation, depending on the mean square errors (MSE's)