Abstract
This paper deals with some Bayes estimators of the parameters of Gamma distribution under different loss functions, represented by Squared-error loss function, Entropy loss function and Scale invariant squared error loss function,with assuming Gamma and Exponential priors for the shape and scale parameters respectively.
Moment, Maximum likelihood estimators and Lindley's approximation are used to obtain the Bayes estimates of the shape and scale parameters of Gamma distribution. Through Monte Carlo simulation method, those estimators have been compared based on the mean squared errors (MSE’s). The results show that, the performance of the Bayes estimators under Scale invariant squared error loss functiongivesfunction produces the best estimates for the two parameters, in all cases.
Keywords: Gamma distribution; Squared-Error loss function; Entropy loss function; Scale invariant squared error loss function; Lindley’s approximation
1. Introduction
Gamma distribution plays an important role in statistical inferential problems. It is widely used in reliability analysis and life testing and as a conjugate prior in Bayesian statistics. It is a good alternative to the popular Weibull distribution. Also, it is a flexible distribution that commonly offers a good fit to any variable such as in environmental research, meteorology, climatology and other physical situationsituations [1].
The probability density function of the Gamma distribution is defined as followfollows: