¹Universidad de São Paulo, Instituto de Matemática y Estadística, Departamento de Estadística, São Paulo, Brasil. Estudiante de doctorado. Email: fhernanb@ime.usp.br
²Universidad de São Paulo, Instituto de Matemática y Estadística, Departamento de Estadística, São Paulo, Brasil. Universidad de Antioquia, Facultad de Ingenierías, Ingeniería Industrial, Medellín, Colombia. Profesora asistente. Email: ousuga@udea.edu.co

Existen varias versiones de la distribución lognormal en la literatura estadística y una de ellas está basada en la transformación exponencial de la distribución normal generalizada (NG). En el presente artículo se presenta el análisis Bayesiano para la distribución lognormal generalizada (logNG) considerando distribuciones a priori de Jeffreys independientes para los parámetros; así como el procedimiento para implementar el muestreador de Gibbs que permite obtener las distribuciones a posteriori de los parámetros. Los resultados obtenidos son usados para analizar modelos de tiempo de falla con datos no censurados y censurados a derecha Tipo I. El procedimiento propuesto es ilustrado usando una base de datos real relacionada con tiempos de falla de computadores.

Palabras clave: análisis de tiempo de falla, censura a derecha, distribución lognormal generalizada, inferencia bayesiana, muestreador de Gibbs.

There are several versions of the lognormal distribution in the statistical literature, one is based in the exponential transformation of generalized normal distribution (GN). This paper presents the Bayesian analysis for the generalized lognormal distribution (logGN) considering independent non-informative Jeffreys distributions for the parameters as well as the procedure for implementing the Gibbs sampler to obtain the posterior distributions of parameters. The results are used to analyze failure time models with right-censored and uncensored data. The proposed method is illustrated using actual failure time data of computers.

Key words: Bayesian inference, Failure time analysis, Gibbs sampling, Lognormal distribution, Right censoring.

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