March 2024 Objective Bayesian analysis for the differential entropy of the Gamma distribution
Eduardo Ramos, Osafu A. Egbon, Pedro L. Ramos, Francisco A. Rodrigues, Francisco Louzada
Author Affiliations +
Braz. J. Probab. Stat. 38(1): 53-73 (March 2024). DOI: 10.1214/23-BJPS591


The paper introduces a fully objective Bayesian analysis to obtain the posterior distribution of an entropy measure. Notably, we consider the gamma distribution, which describes many natural phenomena in physics, engineering, and biology. We reparametrize the model in terms of entropy, and different objective priors are derived, such as Jeffreys prior, reference prior, and matching priors. Since the obtained priors are improper, we prove that the obtained posterior distributions are proper and that their respective posterior means are finite. An intensive simulation study is conducted to select the prior that returns better results regarding bias, mean square error, and coverage probabilities. The proposed approach is illustrated in two datasets: the first relates to the Achaemenid dynasty reign period, and the second describes the time to failure of an electronic component in a sugarcane harvest machine.

Funding Statement

The data and computer codes that support the findings of this study are openly available on GitHub at


Eduardo Ramos acknowledges financial support from São Paulo State Research Foundation (FAPESP Proc. 2019/27636-9). Francisco Rodrigues acknowledges financial support from CNPq (grant number 309266/2019-0). Francisco Louzada is supported by the Brazilian agencies CNPq (grant number 308849/2021-3) and FAPESP (grant number 2013/07375-0).


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Eduardo Ramos. Osafu A. Egbon. Pedro L. Ramos. Francisco A. Rodrigues. Francisco Louzada. "Objective Bayesian analysis for the differential entropy of the Gamma distribution." Braz. J. Probab. Stat. 38 (1) 53 - 73, March 2024.


Received: 1 January 2022; Accepted: 1 November 2023; Published: March 2024
First available in Project Euclid: 4 March 2024

MathSciNet: MR4718425
Digital Object Identifier: 10.1214/23-BJPS591

Keywords: Bayesian analysis , gamma distribution , Matching prior , reference prior , Shannon entropy

Rights: Copyright © 2024 Brazilian Statistical Association


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Vol.38 • No. 1 • March 2024
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