Serviços Personalizados
Journal
Artigo
Inglês (pdf)
Artigo em XML
Referências do artigo
Tradução automática
Enviar este artigo por emailIndicadores
-
Citado por SciELO -
Acessos
Links relacionados
-
Citado por Google -
Similares em
SciELO -
Similares em Google
Compartilhar
Permalink
Revista Colombiana de Estadística
versão impressa ISSN 0120-1751
Rev.Colomb.Estad. vol.42 no.1 Bogotá jan./jun. 2019 Epub 23-Maio-2019
https://doi.org/10.15446/rce.v42n1.71780
Artículos originales de investigación
A Method to Select Bivariate Copula Functions
Un método para seleccionar funciones cópula bivariadas
1 Escuela de Estadística, Facultad de Ingeniería, Universidad del Valle, Cali, Colombia. jose.r.tovar@correounivalle.edu.co
2 Departamento de ciencias naturales y matemáticas, Pontificia Universidad Javeriana, Cali, Colombia. jennyfer.portilla@javerianacali.edu.co
3 Faculdade de Medicina, Universidade de São Paulo, Ribeirão Preto SP, Brazil. achcar@fmrp.usp.br
Copula functions have been extensively used in applied statistics, becoming a good alternative for modeling the dependence of multivariate data. Each copula function has a different dependence structure. An important issue in these applications is the choice of an appropriate copula function model for each case where standard classical or Bayesian discrimination methods could be not appropriate to decide by the best copula. Considering only the special case of bivariate data, we propose a procedure obtained from a recently dependence measure introduced in the literature to select an appropriate copula for the statistical data analyses.
Key words: Copula functions; Discrimination of copulas; Dependence measure; Ledwina measure; Selection method
Las funciones de la cópula se han utilizado ampliamente en las estadísticas aplicadas, convirtiéndose en una buena alternativa para modelar la dependencia de los datos multivariados. Cada función de la cópula tiene una estructura de dependencia diferente. Un tema importante en estas aplicaciones es la elección de un modelo de función de cópula apropiado para cada caso en el que los métodos de discriminación clásicos o bayesianos estándar no sean apropiados para decidir por la mejor cópula. Considerando solo el caso especial de datos bivariados, proponemos un procedimiento obtenido a partir de una medida de dependencia recientemente introducida en la literatura para seleccionar una cópula apropiada para los análisis de datos estadísticos.
Palabras clave: Discriminación de cópulas; Funciones de cópula; Medida de dependencia; Medida de Ledwina; Método de selección
References
Arbenz, P. (2013), 'Bayesian copulae distributions, with application to operational risk management-some comments', Methodology and computing in applied probability 15(1), 105-108. [ Links ]
Bairamov, I., Kotz, S. & Kozubowski, T. (2003), 'A new measure of linear local dependence', Statistics: A Journal of Theoretical and Applied Statistics 37(3), 243-258. [ Links ]
Balakrishnan, N. & Lai, C.-D. (2009), Continuous Bivariate Distributions, Springer, Dordrecht. [ Links ]
Barnett, V. (1980), 'Some bivariate uniform distributions', Communications in statistics-theory and methods 9(4), 453-461. [ Links ]
Bjerve, S. & Doksum, K. (1993), 'Correlation curves: measures of association as functions of covariate values', The Annals of Statistics pp. 890-902. [ Links ]
Chang, K.-L. (2012), 'The time-varying and asymmetric dependence between crude oil spot and futures markets: Evidence from the mixture copula-based arji-garch model', Economic Modelling 29(6), 2298-2309. [ Links ]
Clayton, D. G. (1978), 'A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence', Biometrika 65(1), 141-151. [ Links ]
Corbella, S. & Stretch, D. D. (2013), 'Simulating a multivariate sea storm using archimedean copulas', Coastal Engineering 76, 68-78. [ Links ]
Deheuvels, P. (1981), 'An asymptotic decomposition for multivariate distribution free tests of independence', Journal of Multivariate Analysis 11(1), 102-113. [ Links ]
Drouet, M. & Kotz, S. (2001), Correlation and dependence, Imperial College Press, London. [ Links ]
Durante, F. & Sempi, C. (2015), Principles of copula theory, Chapman and Hall/CRC. [ Links ]
Frank, M. J. (1979), 'On the simultaneous associativity of f(x; y) and x + y - f(x; y)', Aequationes Mathematicae 19(1), 194-226. [ Links ]
Genest, C. & Rémillard, B. (2004), 'Test of independence and randomness based on the empirical copula process', Test 13(2), 335-369. [ Links ]
Goethals, K., Janssen, P. & Duchateau, L. (2008), 'Frailty models and copulas: similarities and di-erences', Journal of Applied Statistics 35(9), 1071-1079. [ Links ]
Gumbel, E. J. (1960a), 'Bivariate exponential distributions', Journal of the American Statistical Association 55(292), 698-707. [ Links ]
Gumbel, E. J. (1960b), 'Distributions des valeurs extremes en plusiers dimensions', Institut de statistique de l'Universite? de Paris 9, 171-173. [ Links ]
Gumbel, E. J. (1961), 'Bivariate logistic distributions', Journal of the American Statistical Association 56(294), 335-349. [ Links ]
Hofert, M. (2008), 'Sampling archimedean copulas', Computational Statistics & Data Analysis 52(12), 5163-5174. [ Links ]
Hougaard, P. (1986), 'A class of multivanate failure time distributions', Biometrika 73(3), 671-678. [ Links ]
Janga Reddy, M. & Ganguli, P. (2012), 'Risk assessment of hydroclimatic variability on groundwater levels in the manjara basin aquifer in india using archimedean copulas', Journal of Hydrologic Engineering 17(12), 1345-1357. [ Links ]
Jogdeo, K. (1982), 'Concepts of dependence', Encyclopedia of statistical sciences 2, 324-334. [ Links ]
Johnson, N. & Kotz, S. (1972), Distributions in Statistics: Continuous Multivariate Distributions, Wileg. [ Links ]
Kojadinovic, I., Yan, J. & Holmes, M. (2011), 'Fast large-sample goodness-of-fit tests for copulas', Statistica Sinica pp. 841-871. [ Links ]
Kowalczyk, T., Pleszczynska, E. et al. (1977), 'Monotonic dependence functions of bivariate distributions', The Annals of Statistics 5(6), 1221-1227. [ Links ]
Lancaster, H. O. (1982), 'Dependence, measures and indices', Encyclopedia of statistical sciences 2, 334-339. [ Links ]
Ledwina, T. (2015), Visualizing association structure in bivariate copulas using new dependence function, in 'Stochastic Models, Statistics and Their Applications', Springer, pp. 19-27. [ Links ]
Lojowska, A., Kurowicka, D., Papaefthymiou, G., van der Sluis, L. et al. (2012), 'Stochastic modeling of power demand due to evs using copula', IEEE Transactions on Power Systems 27(4), 1960. [ Links ]
Meintanis, S. G. (2007), 'Test of -t for marshallolkin distributions with applications', Journal of Statistical Planning and inference 137(12), 3954-3963. [ Links ]
Nelsen, R. B. (2006), An introduction to copulas, Springer. [ Links ]
Sklar, M. (1959), 'Fonctions de repartition an dimensions et leurs marges', Institut de statistique de l'Universite? de Paris 8, 229-231. [ Links ]
Topçu, Ç. (2016), 'Comparison of some selection criteria for selecting bivariate archimedean copulas', Afyon Kocatepe University Journal of Sciences and Engineering 16, 250-255. [ Links ]
Tovar, J. R. & Achcar, J. A. (2012), 'Two dependent diagnostic tests: Use of copula functions in the estimation of the prevalence and performance test parameters', Revista Colombiana de Estadística 35(3), 331-347. [ Links ]
Tovar, J. R. & Achcar, J. A. (2013), 'Dependence between two diagnostic tests with copula function approach: a simulation study', Communications in Statistics-Simulation and Computation 42(2), 454-475. [ Links ]
Wang, Y.-C., Wu, J.-L. & Lai, Y.-H. (2013), 'A revisit to the dependence structure between the stock and foreign exchange markets: A dependence-switching copula approach', Journal of Banking & Finance 37(5), 1706-1719. [ Links ]
Weiss, G. (2011), 'Copula parameter estimation by maximum-likelihood and minimum-distance estimators: a simulation study', Computational Statistics 26(1), 31-54. [ Links ]
Xie, K., Li, Y. & Li, W. (2012), 'Modelling wind speed dependence in system reliability assessment using copulas', IET Renewable Power Generation 6(6), 392-399. [ Links ]
Zhang, Q., Xiao, M., Singh, V. P. & Chen, X. (2013), 'Copula-based risk evaluation of droughts across the pearl river basin, china', Theoretical and applied climatology 111(1-2), 119-131. [ Links ]
Received: April 2018; Accepted: November 2018
This is an open-access article distributed under the terms of the Creative Commons Attribution License
