Classical and Bayesian Estimations on the Exponentiated Gamma Distribution Using Grouped and Un-Grouped Data

In this paper, first we derived classical and Bayesian estimators for the shape parameter of the Exponentiated Gamma distribution using un-grouped data, and also consider relationship between they. We show how the classical estimators can be derived from various choices made within a Bayesian framework. We compare the classical estimators based on their mean squared errors (MSE's). Then, we obtain Bayesian and non-Bayesian estimators of the shape parameter of this distribution under Grouped data. In Bayesian estimation, we consider two types of loss functions; the Squared Error and Precautionary loss functions which are symmetric and asymmetric, respectively. In all cases, we considered both point and interval estimations. These the point and interval estimations are compared empirically using Monte-Carlo simulation.