Estimating the Gumbel-Barnett Copula Parameter of Dependence

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,...

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Main Authors: Jennyfer Portilla Yela, José Rafael Tovar Cuevas
Format: Article
Language:English
Published: Universidad Nacional de Colombia
Series:Revista Colombiana de Estadística
Subjects:
Online Access:http://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0120-17512018000100053&lng=en&tlng=en
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spelling doaj-85ad084a93584268b524201b9a1b0d942020-11-25T03:00:59ZengUniversidad Nacional de Colombia Revista Colombiana de Estadística0120-1751411537310.15446/rce.v41n1.64900S0120-17512018000100053Estimating the Gumbel-Barnett Copula Parameter of DependenceJennyfer Portilla YelaJosé Rafael Tovar CuevasAbstract 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.http://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0120-17512018000100053&lng=en&tlng=enBayesianCopulaCorrelationDependenceEstimationGB copulaSimulation
collection DOAJ
language English
format Article
sources DOAJ
author Jennyfer Portilla Yela
José Rafael Tovar Cuevas
spellingShingle Jennyfer Portilla Yela
José Rafael Tovar Cuevas
Estimating the Gumbel-Barnett Copula Parameter of Dependence
Revista Colombiana de Estadística
Bayesian
Copula
Correlation
Dependence
Estimation
GB copula
Simulation
author_facet Jennyfer Portilla Yela
José Rafael Tovar Cuevas
author_sort Jennyfer Portilla Yela
title Estimating the Gumbel-Barnett Copula Parameter of Dependence
title_short Estimating the Gumbel-Barnett Copula Parameter of Dependence
title_full Estimating the Gumbel-Barnett Copula Parameter of Dependence
title_fullStr Estimating the Gumbel-Barnett Copula Parameter of Dependence
title_full_unstemmed Estimating the Gumbel-Barnett Copula Parameter of Dependence
title_sort estimating the gumbel-barnett copula parameter of dependence
publisher Universidad Nacional de Colombia
series Revista Colombiana de Estadística
issn 0120-1751
description 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.
topic Bayesian
Copula
Correlation
Dependence
Estimation
GB copula
Simulation
url http://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0120-17512018000100053&lng=en&tlng=en
work_keys_str_mv AT jennyferportillayela estimatingthegumbelbarnettcopulaparameterofdependence
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