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

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.

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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