In the current study, the researchers have been obtained Bayes estimators for the shape and scale parameters of Gamma distribution under the precautionary loss function, assuming the priors, represented by Gamma and Exponential priors for the shape and scale parameters respectively. Moment, Maximum likelihood estimators and Lindley’s approximation have been used effectively in Bayesian estimation. Based on Monte Carlo simulation method, those estimators are compared depending on the mean squared errors (MSE’s). The results show that, the performance of Bayes estimator under precautionary loss function with Gamma and Exponential priors is better than other estimates in all cases.

This paper deals with, Bayesian estimation of the parameters of Gamma distribution under Generalized Weighted loss function, based on Gamma and Exponential priors for the shape and scale parameters, respectively. Moment, Maximum likelihood estimators and Lindley’s approximation have been used effectively in Bayesian estimation. Based on Monte Carlo simulation method, those estimators are compared in terms of the mean squared errors (MSE’s).

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.