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Revista Colombiana de Estadística

Print version ISSN 0120-1751

Rev.Colomb.Estad. vol.31 no.2 Bogotá July./Dec. 2008

 

Generación de tiempos de falla dependientes Weibull bivariados usando cópulas

Generation of Weibull Bivariate Dependent Failure Times Using Copulas

MARIO CÉSAR JARAMILLO1, CARLOS MARIO LOPERA2, EVA CRISTINA MANOTAS3, SERGIO YÁÑEZ4

1Universidad Nacional de Colombia, Facultad de Ciencias, Departamento de Estadística, Medellín, Colombia. Profesor Asociado. Email: mcjarami@unal.edu.co
2Universidad Nacional de Colombia, Facultad de Ciencias, Departamento de Estadística, Medellín, Colombia. Profesor Asistente. Email: cmlopera@unal.edu.co
3Universidad Nacional de Colombia, Facultad de Ciencias, Departamento de Estadística, Medellín, Colombia. Profesor Asistente. Email: ecmanota@unal.edu.co
4Universidad Nacional de Colombia, Facultad de Ciencias, Departamento de Estadística, Medellín, Colombia. Profesor Asociado. Email: syanez@unal.edu.co


Resumen

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.

Palabras clave: distribución bivariada, datos dependientes, cópula.


Abstract

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.

Key words: Bivariate distribution, Dependent data, Copula.


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[Recibido en diciembre de 2007. Aceptado en septiembre de 2008]

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

@ARTICLE{RCEv31n2a03,
    AUTHOR  = {Jaramillo, Mario César and Lopera, Carlos Mario and Manotas, Eva Cristina and Yáñez, Sergio},
    TITLE   = {{Generación de tiempos de falla dependientes Weibull bivariados usando cópulas}},
    JOURNAL = {Revista Colombiana de Estadística},
    YEAR    = {2008},
    volume  = {31},
    number  = {2},
    pages   = {169-181}
}

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