Bayesian Prediction and Comparisons of Gompertz Distribution Based on Type-II Censored Data

Abstract

This paper presents the Bayesian Prediction via importance sampling technique (IS) of the Gompertz distribution based on Type-II censored data with square error loss function and LINEX Loss Function. The maximum likelihood method (MLE) could not give the estimation of the shape parameter in the closed forms; therefore, it was solved by the numerical methods. Similarly, the Bayesian estimates and prediction of the parameters could not be solved analytically. Hence, IS is used, where the full conditional distribution for the parameters of Gompertz distribution are obtained. The methods are compared to MLE and the comparisons are made with respect to the Mean Square Error (MSE) to determine the better method in scale and shape parameters of the Gompertz distribution based on Type-II censored data with square error loss function and LINEX Loss Function. The Bayesian of one - sample prediction and two – sample prediction are used to predict the future samples.