Bayes Analysis for the Scale Parameter of Gompertz Distribution

Abstract

In this paper, we investigate the behavior of the bayes estimators, for the scale parameter of the Gompertz distribution under two different loss functions such as, the squared error loss function, the exponential loss function (proposed), based different double prior distributions represented as erlang with inverse levy prior, erlang with non-informative prior, inverse levy with non-informative prior and erlang with chi-square prior.

The simulation method was fulfilled to obtain the results, including the estimated values and the mean square error (MSE) for the scale parameter of the Gompertz distribution, for different cases for the scale parameter of the Gompertz distribution, with different samples sizes. The estimates have been compared in terms of their mean-squared error (MSE).

The results of this paper show that bayes estimators of the scale parameter  of the Gompertz distribution, under the exponential loss function (proposed) are superior to the bayes estimators  under  the squared error loss function , based on erlang-chi-square double prior with  for  all samples sizes  and for all the true values of , in terms of their mean-squared error (MSE)