Análisis bayesiano para la distribución lognormal generalizada aplicada a modelos de falla con censura

• FREDDY HERNÁNDEZ ^[1] ; OLGA CECILIA USUGA ^[1]
  1. [1] Universidad de São Paulo Instituto de Matemática y Estadística Departamento de Estadística
• Localización: Revista Colombiana de Estadística, ISSN-e 2389-8976, ISSN 0120-1751, Vol. 34, Nº. 1, 2011, págs. 95-109
• Idioma: español
• Títulos paralelos:
  • Bayesian Analysis for the Generalized Lognormal Distribution Applied to Failure Time Analysis
• Enlaces
  • Texto completo
• Dialnet Métricas: 1 Cita
• Resumen
  • español

    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.

  • English

    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.

• Referencias bibliográficas
  • Adam, J.. (1962). `Failure time distribution estimation´. Semiconductor Reliability. 2. 41-52
  • Aitchison, J.,Brown, J.. (1957). The Lognormal Distribution. Cambridge University Press.
  • Barrera, C.,Correa, J.. (2008). `Distribuci\'on predictiva bayesiana para modelos de pruebas de vida v\'\ia MCMC´. Revista Colombiana...
  • Berger, J.. (1985). Statistical Decision Theory and Bayesian Analysis. Springer.
  • Bernardo, J.. (1979). `Expected information as expected utility´. Annals of Statistics. 7. 686-690
  • Chen, G.. (1995). `Generalized log-normal distributions with reliability application´. Computational Statistics and Data Analysis. 19....
  • Chen, K.,Papadopoulos, A.. (1997). `Shortest Bayes credibility intervals for the lognormal failure model´. Microelectron Reliability....
  • Gamerman, D.,Lopes, H.. (2006). Markov Chain Monte Carlo Stocastic Simulation for Bayesian Inference. Chapman and Hall/CRC.
  • Gelman, A.,Stern, J.,Rubin, H.. (2004). Bayesian Data Analysis. Chapman & Hall-CRC.
  • Gupta, R.,Lvin, S.. (2005). `Reliability functions of generalized log-normal model´. Mathematical and Computer Modelling. 42. 939-946
  • Hoff, P.. (2009). A First Course in Bayesian Statistical Methods. Springer.
  • Howard, B.,Dodson, G.. (1961). `High stress aging to failure of semiconductor devices´. Proc. Seventh National Symposium on Reliability...
  • Klein, J.,Moeschberger, M.. (2003). Survival Analysis: Techniques for Censored and Truncated Data. Springer-Verlag.
  • Lawless, J. F.. (1982). Statistical Models and Methods for Lifetime Data. Wiley.
  • Mart\'\in, J.,P\'erez, C.. (2009). `Bayesian analysis of a generalized lognormal distribution´. Computational Statistics and Data...
  • Nadarajah, S.. (2005). `A generalized normal distribution´. Journal of Applied Statistics. 37. 685-694
  • Padgett, W.,Johnson, M.. (1983). `Lower bounds on reliability in the lognormal distribution´. The Canadian Journal of Statistics - La...
  • Portela, J.,G\'omez-Villegas, M.. (2004). `Implementation of a robust Bayesian method´. Journal of Statistical Computation and Simulation....
  • (2010). R Development Core Team, R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing. Vienna.
  • Robert, C.. (2001). The Bayesian Choice. Springer.
  • Spiegelhalter, D.,Best, N.,Carlin, B.,van der Linde, A.. (2002). `Bayesian measures of model complexity and fit´. Journal of The Royal...
  • Upadhyay, S.,Peshwani, M.. (2001). `Full posterior analysis of three parameter Lognormal distribution using Gibbs sampler´. Journal of...
  • Upadhyay, S.,Peshwani, M.. (2003). `Choice between Weibull and lognormal models: a simulation based Bayesian study´. Communications in...
  • Upadhyay, S.,Peshwani, M.. (2008). `Posterior analysis of lognormal regressions models using the Gibbs sampler´. Statistical Papers. 49....