Bayes Estimators for the Shape Parameter of Pareto Type I Distribution under Generalized Square Error Loss Function

Abstract

In this paper, we obtained Basyian estimators of the shape parameter of the Pareto type I distribution using Bayian method under Generalized square error loss function and Quadratic loss function. In order to get better understanding of our Bayesian analysis we consider non-informative prior for the shape parameter Using Jeffery prior Information as well as informative prior density represented by Exponential distribution. These Bayes estimators of the shape parameter of the Pareto type I distribution are compared with some classical estimators such as, the Maximum likelihood estimator (MLE), the Uniformly minimum variance unbiased estimator (UMVUE), and the Minimum mean squared error (MinMSE) estimator according to Monte-Carlo simulation study. The performance of these estimators is compared by employing the mean square errors (MSE’s).

Key words: Pareto distribution; Maximum likelihood estimator; Uniformly minimum variance unbiased estimator; Minimum mean squared error; Bayes estimator; Generalized square error loss function; Quadratic loss function; Jeffery prior; Exponential prior.