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Revista Colombiana de Estadística

Print version ISSN 0120-1751

Rev.Colomb.Estad. vol.36 no.2 Bogotá June/Dec. 2013


Bayesian Inference for Two-Parameter Gamma Distribution Assuming Different Noninformative Priors

Inferencia Bayesiana para la distribución Gamma de dos parámetros asumiendo diferentes a prioris no informativas


1Universidade Estadual Paulista, Facultad de Ciencia y Tecnología, Departamento de Estadística, Presidente Prudente, Brasil. Professor. Email:
2Universidade Estadual Paulista, Facultad de Ciencia y Tecnología, Departamento de Estadística, Presidente Prudente, Brasil. Student. Email:
3Universidade de São Paulo, Facultad de Medicina de Ribeirão Preto, Departamento de Medicina Social, Ribeirão Preto, Brasil. Professor. Email:


In this paper distinct prior distributions are derived in a Bayesian inference of the two-parameters Gamma distribution. Noniformative priors, such as Jeffreys, reference, MDIP, Tibshirani and an innovative prior based on the copula approach are investigated. We show that the maximal data information prior provides in an improper posterior density and that the different choices of the parameter of interest lead to different reference priors in this case. Based on the simulated data sets, the Bayesian estimates and credible intervals for the unknown parameters are computed and the performance of the prior distributions are evaluated. The Bayesian analysis is conducted using the Markov Chain Monte Carlo (MCMC) methods to generate samples from the posterior distributions under the above priors.

Key words: Gamma distribution, noninformative prior, copula, conjugate, Jeffreys prior, reference, MDIP, orthogonal, MCMC.


En este artículo diferentes distribuciones a priori son derivadas en una inferencia Bayesiana de la distribución Gamma de dos parámetros. A prioris no informativas tales como las de Jeffrey, de referencia, MDIP, Tibshirani y una priori innovativa basada en la alternativa por cópulas son investigadas. Se muestra que una a priori de información de datos maximales conlleva a una a posteriori impropia y que las diferentes escogencias del parámetro de interés permiten diferentes a prioris de referencia en este caso. Datos simulados permiten calcular las estimaciones Bayesianas e intervalos de credibilidad para los parámetros desconocidos así como la evaluación del desempeño de las distribuciones a priori evaluadas. El análisis Bayesiano se desarrolla usando métodos MCMC (Markov Chain Monte Carlo) para generar las muestras de la distribución a posteriori bajo las a priori consideradas.

Palabras clave: a prioris de Jeffrey, a prioris no informativas, conjugada, cópulas, distribución Gamma, MCMC, MDIP, ortogonal, referencia.

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[Recibido en enero de 2013. Aceptado en septiembre de 2013]

Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

    AUTHOR  = {Antonio Moala, Fernando and Luiz Ramos, Pedro and Alberto Achcar, Jorge},
    TITLE   = {{Bayesian Inference for Two-Parameter Gamma Distribution Assuming Different Noninformative Priors}},
    JOURNAL = {Revista Colombiana de Estadística},
    YEAR    = {2013},
    volume  = {36},
    number  = {2},
    pages   = {319-336}