Copulas and Extreme Values

This lecture discusses the use of copulas to measure the strength of dependence in distributions, focusing on distinguishing between different rates of convergence to zero. It covers the concept of X(u) as a measure of dependence level, the scaling chosen for independent and dependent variables, and the distinction between perfectly and asymptotically dependent variables. The lecture also explores the application of copulas in extreme value theory, transforming variables to unit Fréchet margins, and the limiting distribution of componentwise maxima. Examples with bivariate normal and Student t distributions are provided to illustrate the concepts.