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Revista Colombiana de Estadística
Print version ISSN 0120-1751
Rev.Colomb.Estad. vol.46 no.1 Bogotá Jan./June 2023 Epub Jan 18, 2023
https://doi.org/10.15446/rce.v46nl.95989
Original articles of research
Objective Prior Distributions to Estimate the Parameters of the Poisson-Exponential Distribution
Distribuciones previas objetivas para estimar los parámetros de la distribución Poisson-Exponencial
1 Departamento de Estatística, Faculdade de Ciências e Tecnologia, Universidade Estadual Paulista, São Paulo, Brasil
In this paper, a set of important objective priors are examined for the Bayesian estimation of the parameters present in the Poisson-Exponential distribution PE. We derived the multivariate Jeffreys prior and the Maxi-mal Data Information Prior. Reference prior and others priors proposed in the literature are also analyzed. We show that the posterior densities resulting from these approaches are proper although the respective priors are improper. Monte Carlo simulations are used to compare the efficiencies and to assess the sensitivity of the choice of the priors, mainly for small sample sizes. This simulation study shows that the mean square error, mean bias and coverage probability of credible intervals under Gamma, Jeffreys' rule and Box & Tiao priors presented equal results, whereas Jeffreys and Reference priors showed the best results. The MDIP prior had a worse performance in all analyzed situations showing not to be indicated for Bayesian analysis of the PE distribution. A real data set is analyzed for illustrative purpose of the Bayesian approaches.
Key words: Bayesian; Poisson-Exponential; Jeffreys; MDIP; Objective; Prior
En este artículo, se examina un conjunto de importantes priori objetivas para la estimación bayesiana de los parámetros de la distribución Poisson-Exponencial (PE). Derivamos la priori Jeffreys multivariada y la Maximal Data Information Prior. También se analizan la priori de Referencia y otras prioris propuestas en la literatura. Mostramos que las distribuciones posterioris resultantes de estos enfoques son adecuadas, aunque las respectivas prioris son impropias. Las simulaciones de Monte Carlo se utilizan para comparar las eficiencias, para evaluar la sensibilidad de la elección de las prioris, principalmente para tamaños de muestra pequeños. Este estudio de simulación muestra que los errores cuadráticos medios, el sesgo medio y la probabilidad de cobertura de los intervalos creíbles bajo la Gamma, regla de Jeffreys y Box & Tiao mostraron resultados iguales, mientras que los prioris de Jeffreys y Reference mostraron los mejores resultados. El priori MDIP tuvo un peor desempeño en todas las situaciones analizadas mostrando no estar indicado para el análisis bayesiano de la distribución PE. Se analiza un conjunto de datos reales con fines ilustrativos de los enfoques bayesianos.
Palabras clave: Bayesiano; Jeffreys; MDIP; Objetiva; Poisson-Exponencial; Priori
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Received: May 2022; Accepted: November 2022
This is an open-access article distributed under the terms of the Creative Commons Attribution License
