Copulas: Properties and Applications

This lecture introduces copulas, which are distribution functions on [0, 1] with standard uniform marginal distributions. It covers the properties of copulas, such as the rectangle inequality and invariance under strictly increasing transformations. The lecture also discusses Sklar's Theorem, which shows the implicit use of copulas in multivariate distributions. Furthermore, it explores the concept of meta distributions, Gaussian copulas, and various dependence measures like linear correlation, rank correlations (Kendall's tau and Spearman's rho), and coefficients of tail dependence. The lecture concludes with a discussion on fallacies related to rank correlations and the parametrization of copulas.