Bayes Estimator of the Shape Parameter of Generalized Exponential Distribution

Abstract

Bayes estimators for the shape parameter of generalized exponential distribution are obtained. Two prior density functions, Jeffery prior information and gamma conjugate prior were used to find the Bayes estimators. LINEX (linear-exponential) error loss function was considered. Simulation study was designed and mean square error criterion was used to compare between the two methods. The results show that the estimators with gamma conjugate prior density function were better than the estimators with Jeffery prior density function at all sample sizes. In addition Bayes estimators with two types of prior density function had lower mean square errors than maximum likelihood estimator for all sample sizes.