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The present paper introduces a fully objective Bayesian analysis to obtainthe posterior distribution of an entropy measure. Notably, we consider thegamma distribution, which describes many natural phenomena in physics,engineering, and biology. We reparametrize the model in terms of entropy, anddifferent objective priors are derived, such as Jeffreys prior, referenceprior, and matching priors. Since the obtained priors are improper, we provethat the obtained posterior distributions are proper and that their respectiveposterior means are finite. An intensive simulation study is conducted toselect the prior that returns better results regarding bias, mean square error,and coverage probabilities. The proposed approach is illustrated in twodatasets: the first relates to the Achaemenid dynasty reign period, and thesecond describes the time to failure of an electronic component in a sugarcaneharvest machine.

Objective Bayesian Analysis for the Differential Entropy of the Gamma Distribution