Published

2018-01-01

Estimating the Gumbel-Barnett copula parameter of dependence

Estimación del parámetro de dependencia de la copula Gumbel-Barnett

DOI:

https://doi.org/10.15446/rce.v41n1.64900

Keywords:

Copula, Dependence, Correlation, Estimation, Bayesian, Simulation (en)
bayesiana, copula Gumbel Barnett, correlación, dependencia copula, estimación, simulación (es)

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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.
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\linebreak el mejor desempeño sin importar el tamaño de muestra y la estructura de dependencia.

References

Balakrishnan, N. & Lai, C.-D. (2009), Continuous bivariate distributions, Springer Science & Business Media.

Barnett, V. (1980), `Some bivariate uniform distributions', Communi

ations in statistics-theory and methods 9(4), 453-461.

Barnett, V. (1983), `Redued distance measures and transformations in processing multivariate outliers', Australian & New Zealand Journal of Statistics 25(1), 64-75.

Efron, B. (1992), Bootstrap methods: another look at the ja

kknife, in `Breakthroughs in Statistics', Springer, pp. 569-593.

Genest, C., Ghoudi, K. & Rivest, L.-P. (1995), `A semiparametri

estimation procedure of dependence parameters in multivariate families of distributions', Biometrika pp. 543-552.

Genest, C. & Mackay, R. J. (1986), `Copules archimédiennes et families de lois bidimensionnelles dont les marges sont données', Canadian Journal of Statistics 14(2), 145-159.

Gumbel, E. J. (1960), `Bivariate exponential distributions', Journal of the American Statistical Association 55(292), 698-707.

Hoff, P. D. (2007), `Extending the rank likelihood for semiparametrica copula estimation', The Annals of Applied Statistics pp. 265-283.

Klein, I. & Christa, F. (2011), Families of copulas closed under the

construction of generalized linear means, Technical report, IWQW discussion paper series.

Louie, H. (2014), `Evaluation of bivariate archimedean and elliptical

copulas to model wind power dependence y structures', Wind Energy 17(2), 225-240.

Martinez, E. Z. & Achcar J. (2014), `Bayesian bivariate generalized lindley model for survival data with a cure fraction', Computer methods and programs in biomedicine 117(2), 145-157.

Mengersen, K. L., Pudlo, P. & Robert, C. P. (2013), `Bayesian computation via empirical likelihood', Proceedings of the National Academy of Sciences 110(4), 1321-1326.

Min, A. & Czado, C. (2010), `Bayesian inference for multivariate

copulas using pair-copula constructions', Journal of Financial Econometrics 8(4), 511-546

Oh, D. H. & Patton, A. J. (2013), `Simulated method of moments estimation for copula-based multivariate models', Journal of the Ameri

an Statistics al Association 108(502), 689-700.

Omidi, M. & Mohammadzadeh, M. (2015), `A new method to build spatiotemporal covariance functions: analysis of ozone data', Statistical Papers (3), 115.

Tovar, J. R. (2012), `Eliciting beta prior distributions for binomial sampling', Rev. Bras. Biom 30(1), 159-172.

Tovar, J. R. & Achcar, J. A. (2011), `Indexes to measure dependence between clinical diagnostics tests: A comparative study', Revista Colombiana de Estadística 34, 433-450.

Tovar, J. R. & Achcar, J. A. (2012), `Two dependent diagnosti

tests: Use of copula functions in the estimation of the prevalence and performane test parameters', Revista Colombiana de Estadística 35(3), 331-347.

Tovar, J. R. & Achcar, J. A. (2013), `Dependence between two diagnosti

tests with copula function approach: a simulation study', Communications in Statistics-Simulation and Computation 42(2), 454-475.

Weib, G. (2011), `Copula parameter estimation by maximum-likelihood and minimum-distance estimators: a simulation study', Computational Statistics 26(1), 31-54.

How to Cite

APA

Portilla Yela, J. & Tovar Cuevas, J. R. (2018). Estimating the Gumbel-Barnett copula parameter of dependence. Revista Colombiana de Estadística, 41(1), 53–73. https://doi.org/10.15446/rce.v41n1.64900

ACM

[1]
Portilla Yela, J. and Tovar Cuevas, J.R. 2018. Estimating the Gumbel-Barnett copula parameter of dependence. Revista Colombiana de Estadística. 41, 1 (Jan. 2018), 53–73. DOI:https://doi.org/10.15446/rce.v41n1.64900.

ACS

(1)
Portilla Yela, J.; Tovar Cuevas, J. R. Estimating the Gumbel-Barnett copula parameter of dependence. Rev. colomb. estad. 2018, 41, 53-73.

ABNT

PORTILLA YELA, J.; TOVAR CUEVAS, J. R. Estimating the Gumbel-Barnett copula parameter of dependence. Revista Colombiana de Estadística, [S. l.], v. 41, n. 1, p. 53–73, 2018. DOI: 10.15446/rce.v41n1.64900. Disponível em: https://revistas.unal.edu.co/index.php/estad/article/view/64900. Acesso em: 15 nov. 2025.

Chicago

Portilla Yela, Jennyfer, and José Rafael Tovar Cuevas. 2018. “Estimating the Gumbel-Barnett copula parameter of dependence”. Revista Colombiana De Estadística 41 (1):53-73. https://doi.org/10.15446/rce.v41n1.64900.

Harvard

Portilla Yela, J. and Tovar Cuevas, J. R. (2018) “Estimating the Gumbel-Barnett copula parameter of dependence”, Revista Colombiana de Estadística, 41(1), pp. 53–73. doi: 10.15446/rce.v41n1.64900.

IEEE

[1]
J. Portilla Yela and J. R. Tovar Cuevas, “Estimating the Gumbel-Barnett copula parameter of dependence”, Rev. colomb. estad., vol. 41, no. 1, pp. 53–73, Jan. 2018.

MLA

Portilla Yela, J., and J. R. Tovar Cuevas. “Estimating the Gumbel-Barnett copula parameter of dependence”. Revista Colombiana de Estadística, vol. 41, no. 1, Jan. 2018, pp. 53-73, doi:10.15446/rce.v41n1.64900.

Turabian

Portilla Yela, Jennyfer, and José Rafael Tovar Cuevas. “Estimating the Gumbel-Barnett copula parameter of dependence”. Revista Colombiana de Estadística 41, no. 1 (January 1, 2018): 53–73. Accessed November 15, 2025. https://revistas.unal.edu.co/index.php/estad/article/view/64900.

Vancouver

1.
Portilla Yela J, Tovar Cuevas JR. Estimating the Gumbel-Barnett copula parameter of dependence. Rev. colomb. estad. [Internet]. 2018 Jan. 1 [cited 2025 Nov. 15];41(1):53-7. Available from: https://revistas.unal.edu.co/index.php/estad/article/view/64900

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CrossRef Cited-by

CrossRef citations3

1. Hüseyin ÜNÖZKAN, Mehmet YILMAZ. (2019). Construction of Continuous Bivariate Distribution by Transmuting Dependent Distribution. Cumhuriyet Science Journal, 40(4), p.860. https://doi.org/10.17776/csj.618236.

2. Aysegul Erem. (2020). Bivariate two sample test based on exceedance statistics. Communications in Statistics - Simulation and Computation, 49(9), p.2389. https://doi.org/10.1080/03610918.2018.1520868.

3. Luis Carlos Bravo Melo, Jennyfer Portilla Yela, José Rafael Tovar Cuevas. (2020). Using Copula Functions to Estimate The AUC for Two Dependent Diagnostic Tests. Revista Colombiana de Estadística, 43(2), p.315. https://doi.org/10.15446/rce.v43n2.80288.

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