Bayesian and Non-Bayesian Parameters Estimation of Gamma distribution at Various Loss Functions

Abstract

This paper deals with some Estimator of Bayes s of the parameters of Gamma distribution (GD) under three different loss functions, represented via Precautionary loss function, Entropy loss function (ELF) and invariant of scale squared error (SE) loss function, assuming Gamma and Exponential priors for the shape and scale parameters respectively. Maximum likelihood estimator (MLE) and Lindley’s approximation are used to obtain the Bayes estimates of the shape and scale parameters of GD. According to the Monte Carlo simulation method, those estimators have been compared based on the mean SEs (MSE’s). The results show that the performance of the Estimator of Bayes s under invariant of scale SE loss function produces the best estimates for the two parameters in all cases.