ABSTRACT
In this chapter we consider the issue of modelling dependence among the components of a random vector using copulas. The main ingredient will be Sklar’s theorem, which is the building block of the theory of copulas, since it allows to connect the probability law of any multivariate random vector to its marginal distributions through a copula. Because of this theorem copulas occupy a relevant position in Probability Theory and Statistics; the first part of this chapter is devoted to Sklar’s theorem and presents several different proofs of it. Then we show how Sklar’s theorem is used in order to express different dependence notions among random variables.
