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Revista Colombiana de Estadística
versão impressa ISSN 0120-1751
Rev.Colomb.Estad. vol.41 no.1 Bogotá jan./jun. 2018
https://doi.org/10.15446/rce.v41n1.64900
Artículos originales de investigación
Estimating the Gumbel-Barnett Copula Parameter of Dependence
Estimación del parámetro de dependencia de la copula Gumbel-Barnett
1Escuela de Estadística, Facultad de Ingeniería, Universidad del Valle, Cali, Colombia.
In this paper, we developed an empirical evaluation of four estimation procedures for the dependence parameter of the Gumbel-Barnett copula obtained from a Gumbel type I distribution. We used the maximum likelihood, moments and Bayesian methods and studied the performance of the estimates, assuming three dependence levels and 20 different sample sizes. For each method and scenario, a simulation study was conducted with 1000 runs and the quality of the estimator was evaluated using four different criteria. A Bayesian estimator assuming a Beta(a; b) as prior distribution, showed the best performance regardless the sample size and the dependence structure.
Key words: Bayesian; Copula; Correlation; Dependence; Estimation; GB copula; Simulation
En este artículo, desarrollamos una evaluación empírica de cuatro procedimientos de estimación para el parámetro de dependencia, de la función copula Gumbel Barnett obtenida a partir de la distribución Gumbel tipo I. Se usó el método de estimación por momentos, el método de la máxima verosimilitud y dos aproximaciones Bayesianas. Se estudió el comportamiento de las estimaciones asumiendo tres niveles de dependencia y 20 tamaños de muestra distintos. Para cada método y escenario formado entre el nivel de dependencia y el tamaño de muestra, se desarrolló un estudio de simulación con 1000 repeticiones y el comportamiento de las estimaciones fue evaluado usando cuatro criterios. El estimador obtenido asumiendo una distribución Beta(a; b) para modelar la información previa, presentó el mejor desempeño sin importar el tamaño de muestra y la estructura de dependencia.
Palabras clave: bayesiana; copula Gumbel Barnett; correlación; dependencia copula; estimación; simulación
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