In this paper, we deal with Bayesian, E-Bayesian and hierarchical Bayesian estimation in a family of distributions under a squared log error loss function. Specially, E-Bayesian and hierarchical Bayesian estimators for the shape parameter of a Pareto distribution is provided when the scale parameter is known. A monte carlo simulation is conducted for comparision of Bayes and E-Bayesian estimators. A real data set is used for illustrating the proposed estimators.
