Empirical Bayes Inference on the Weibull Distribution Parameters Based on the Characteristic Prior

Abstract

Abstract In this study, a new technique has been applied for eliciting the prior density function for the empirical Bayes by utilizing the characteristic function, which frees the Bayesian inference from subjectivity. The empirical Bayes estimates have been studied for the Weibull model parameters based on the characteristic prior and the informative gamma prior in terms of the mean squared errors and the mean percentage errors, via Monte Carlo simulations. The simulation results indicated that the empirical Bayes results based on the characteristic prior outperformed the ones based on the informative gamma prior. Finally, a numerical example is given to demonstrate the efficiency of the proposed priors.