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Revista Colombiana de Estadística

Print version ISSN 0120-1751

Rev.Colomb.Estad. vol.41 no.1 Bogotá Jan./June 2018

http://dx.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

Jennyfer Portilla Yela1  a  , José Rafael Tovar Cuevas1  b 

1Escuela de Estadística, Facultad de Ingeniería, Universidad del Valle, Cali, Colombia.

Abstract

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

Resumen

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

Full text available only in PDF format

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