Copulas: Properties and Applications

This lecture covers copulas, a powerful tool in multivariate statistics, starting with their definition and basic properties, examples, and meta distributions. It explores further properties such as comonotonicity, countermonotonicity, and exchangeability. The lecture delves into linear correlation, fallacies, and Hoeffding's identity. It also discusses copula densities, conditional distributions, and the concept of survival copulas. The presentation concludes with the theorem on attainable correlations and their implications in modeling dependence structures.