Inference and Bayesian Prediction for Gompertz Distribution under Generalized Order Statistics

Abstract

Based on generalized order statistics (gos), the Bayes and the maximum likelihood (ML) estimators have been obtained for parameters, reliability and hazard function from the two-parameter Gompertz distribution. The symmetric (squared error loss (SEL)) and asymmetric loss functions (linear-exponential (LINEX)) are considered for Bayesian estimation. The Bayes estimators of the unknown parameters can not be obtained in closed-form and so we propose to apply Soland’s method and Markov Chain Monte Carlo (MCMC) method to tackle this problem. The Bayesian prediction intervals for gos based on Gompertz distribution are obtained in one sample case. Finally, some numerical results are presented to illustrate the performance of the procedures.