Abstract
Copula distributions are a useful tool to describe dependence between two or more random variables. Sklar’s theorem allows to treat separately the dependence structure (the copula) and the marginal distributions. In the bivariate case, where is the bivariate cumulative distribution function, are the marginal cdfs and is the copula linking the marginals. When the marginal distributions are continuous the copula that links the marginal distributions is unique. There are several copula families, representing different dependence structures. A new copula family, CrEnC copulas, has been studied. This copula family is flexible enough to describe different types of dependence. An application to the spatial dependence of precipitation of two near locations is presented. A data set of 30 years of daily precipitation recorded at two nearby rain gauges located in the Valencia Region, Eastern Spain, has been studied. For each rain gauge, the logarithm of precipitation is modeled using a Generalized Pareto Distribution (GPD). The CrEnC copula family is used to model dependence between both extremal precipitation variables. Bayesian methods are applied to obtain estimations of the model parameters: marginal GPD and CrEnC copula parameters.
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References
Egozcue, J. J., Pawlowsky-Glahn, V., Ortego, M. I., & Tolosana Delgado, R. (2006). The effect of scale in daily precipitation hazard assessment. Natural Hazards and Earth Systems Sciences, 6, 459–470.
Egozcue, J. J., & Ramis, C. (2001). Bayesian hazard analysis of heavy precipitation in eastern Spain. International Journal of Climatology, 21, 1263–1279.
Kullback, S., & Leibler, R. A. (1951). On information and sufficiency. The Annals of Mathematical Statistics, 22(1), 79–86.
Nelsen, R. B. (1999). An introduction to copulas. New York: Springer.
Pawlowsky-Glahn, V., & Egozcue, J. J. (2001). Geometric approach to statistical analysis on the simplex. Stochastic Environmental Research and Risk Assessment, 15(5), 384–398.
Pickands, J., III. (1975). Statistical inference using extreme order statistics. Annals of Statistics, 3(1), 119–131.
Romero, R., Guijarro J. A., Ramis, C., & Alonso, S. (1998). A 30-years (1964–93) daily rainfall data base for the Spanish Mediterranean regions: First exploratory study. International Journal of Climatology, 18,541–560.
Rumsey, H, Jr, & Posner, E. C. (1965). Joint distributions with prescribed moments. The Annals of Mathematical Statistics, 1(36), 286–298.
Schweizer, B., & Wolff, E. F. (1981). On nonparametric measures of dependence for random variables. Annals of Statistics, 9(4), 870–885.
Sklar, A. (1959). Fonctions de répartition à n dimensions et leurs marges. Publications of the Institute of Statistics of the University of Paris, 8(1), 229–231.
Acknowledgments
This research has received funding from the Spanish Government, projects COVARIANCE (CTM2010-19709), CODA-RSS (MTM2009-13272) and Metrics (MTM2012-33236).
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Ortego, M.I., Egozcue, J.J., Tolosana-Delgado, R. (2014). Modeling Extremal Dependence Using Copulas. Application to Rainfall Data. In: Pardo-Igúzquiza, E., Guardiola-Albert, C., Heredia, J., Moreno-Merino, L., Durán, J., Vargas-Guzmán, J. (eds) Mathematics of Planet Earth. Lecture Notes in Earth System Sciences. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32408-6_13
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DOI: https://doi.org/10.1007/978-3-642-32408-6_13
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