The statistical modeling of natural events frequently involves the modeling of the joint distribution of several random phenomena. Copulas are mathematical objects that are particularly suitable for modeling the multivariate dependence between several continuous random variables, independently of their marginal distributions. This explains why they are more and more often used in hydrology and environmental sciences. With the development of powerful statistical software (such as the R statistical system), a multivariate analysis based on copulas appears increasingly feasible. This one-week short course will focus on the theory and statistical practice of copulas with applications to hydrological problems and related environmental issues. It will also contain an introduction to multivariate extreme-value theory from a copula perspective. Theoretical concepts will be illustrated through the analysis of real-world datasets using the R statistical system.
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