Objective Bayesian analysis for the differential entropy of the Weibull distribution

Abstract

This article addresses the estimation of differential entropy of the Weibull distribution based on different non-informative prior distributions. We first derive non-informative priors using formal rules, such as Jeffreys prior and maximal data information prior based on Fisher information and entropy, respectively. We also develop reference prior and probability matching prior for the differential entropy. Next, we investigate the effects of these priors in the Bayes estimates of the differential entropy of the Weibull distribution based on complete sample. The Bayes estimates are computed using random-walk Metropolis-Hastings algorithms. We use Monte Carlo simulation to evaluate the performance of the Bayes estimates of differential entropy in terms of bias and root mean-squared error, while highest posterior density credible intervals are assessed in terms of average width and coverage probabilities. Finally, a real data set has been analyzed for illustrative purposes.