Generación de tiempos de falla dependientes Weibull bivariados usando cópulas

• MARIO CÉSAR JARAMILLO ^[1] ; CARLOS MARIO LOPERA ^[1] ; EVA CRISTINA MANOTAS ^[1] ; SERGIO YÁÑEZ ^[1]
  1. [1] Universidad Nacional de Colombia

     Universidad Nacional de Colombia

     Colombia

     
• Localización: Revista Colombiana de Estadística, ISSN-e 2389-8976, ISSN 0120-1751, Vol. 31, Nº. 2, 2008, págs. 169-181
• Idioma: español
• Títulos paralelos:
  • Generation of Weibull Bivariate Dependent Failure Times Using Copulas
• Enlaces
  • Texto completo
• Dialnet Métricas: 2 Citas
• Resumen
  • español

    La distribución Weibull bivariada es muy importante en confiabilidad y en análisis de supervivencia. La dependencia para este tipo de problemas ha venido cobrando gran importancia en años recientes. En la literatura, se conocen algoritmos para generar una distribución Weibull univariada y distribuciones bivariadas con marginales independientes. En este artículo, se presenta un algoritmo para generar tiempos de falla Weibull bivariados dependientes, usando una representación cópula para la función de confiabilidad Weibull bivariada. Tal representación se obtiene utilizando modelos cópula arquimedianos. En particular, se utilizó la familia Gumbel. Se realizó una aplicación del algoritmo cópula, cuyos resultados fueron validados exitosamente.

  • English

    The bivariate Weibull distribution is very important in both reliability and survival analysis. The dependence for these kind of problems has been gaining great importance in recent years. In the literature, there are algorithms to generate univariate Weibull distributions and bivariate Weibull distributions with independent marginal distributions. In this paper, we present an algorithm to generate dependent bivariate Weibull failure times using a copula representation for the bivariate Weibull reliability function. Such representation is obtained using archimedean copula models. In particular, we used the Gumbels family. An application of the copula algorithm was done and the results were successfully validated.

• Referencias bibliográficas
  • Bedford, T.. (2005). `Modern Statistical and Mathematical Methods in Reliability´. World Scientific Publishing Co.
  • Bouyè, E.,Durrleman, V.,Bikeghbali, A.,Riboulet, G.,Rconcalli, T.. (2000). `Copulas for Finance - A Reading Guide and Some Applications´....
  • (2007). Canty, A. & Ripley, B. D.. Boot: Bootstrap R (S-Plus) Functions (Canty).
  • Chambers, J. M.,Mallows, C. L.,Stuck, B. W.. (1976). `A Method for Simulating Stable Random Variables´. Journal of the American Statistical...
  • Cherubini, U.,Luciano, E.,Vecchiato, W.. (2004). Copula Methods in Finance. John Wiley & Sons.
  • Clayton, D. G.. (1978). `A Model for Association in Bivariate Life Tables and its Application in Epidemiological Studies of Familial Tendency...
  • Conover, W. J.. (1999). Practical Nonparametric Statistics. John Wiley & Sons. New York.
  • Crowder, M.. (2001). Classical Competing Risks. Chapman & Hall. London.
  • Denuit, M.,Dhaene, J.,Goovaerts, M.,Kaas, R.. (2005). Actuarial Theory for Dependent Risks: Measures, Orders and Models. John Wiley &...
  • Embrechts, P.,Lindskog, F.,McNeil, A.. (2003). `Handbook of Heavy Tailed Distribution in Finance´. Elsevier. North-Holland.
  • Escarela, G.,Carrière, J. F.. (2003). `Fitting Competing Risks with an Assumed Copula´. Statistical Methods in Medical Research. 12. 333-349
  • Frank, M. J.. (1979). `On the Simultaneous Associativity of f(x,y) and x + y - f(x,y)´. Aequationes Mathematicae. 19. 194-226
  • Frees, E. W.,Carrière, J. F.,Valdez, E. A.. (1996). `Annuity Valuation with Dependent Mortality´. Journal of Risk and Insurance. 63. 229-261
  • Frees, E. W.,Valdez, E. A.. (1998). `Understanding Relationships Using Copulas´. North American Actuarial Journal. 2. 1-25
  • Frees, E. W.,Wang, P.. (2005). `Credibility Using Copulas´. North American Actuarial Journal. 9. 31-48
  • Genest, C.,Favre, A. C.. (2007). `Everything You Always Wanted to Know About Copula Modeling but were Afraid to Ask´. Journal of Hydrologic...
  • Gumbel, E. J.. (1960). `Bivariate Exponential Distributions´. Journal of the American Statistical Association. 55. 698-707
  • Joe, H.. (1997). Multivariate Models and Dependence Concepts. Chapman & Hall. New York.
  • Lu, J.,Bhattacharyya, G. K.. (1990). `Some New Constructions of Bivariate Weibull Models´. Annals of the Institute of Statistical Mathematics....
  • (2007). Lund, U. & Agostinelli, C.. CircStats: Circular Statistics, from ``Topics in Circular Statistics'' (2001).
  • Nelsen, R. B.. (2006). An Introduction to Copulas. Springer. New York.
  • (2007). R Development Core Team, R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing. Vienna.
  • Samorodnitsky, G.,Taqqu, M. S.. (1994). Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance. Chapman & Hall....
  • Venables, W. N.,Ripley, B. D.. (2002). Modern Applied Statistics with S. Springer. New York.
  • Wang, W.,Wells, M. T.. (2000). `Model Selection and Semiparametric Inference for Bivariate Failure-Time Data´. Journal of the American...
  • Yan, J.. (2006). `Handbook in Engineering Statistics´. Springer. New York.