Extreme-Value Theorems

This lecture covers the Extremal Types Theorem and the Exceedance Theorem, which provide insights into the limiting distributions of maxima and threshold exceedances. The lecture discusses the generalized extreme-value distribution (GEV) and the generalized Pareto distribution (GPD) as natural models for extreme values. It also explores the relationship between GEV and GPD, stability conditions, and the convergence of maxima. The lecture emphasizes the importance of stability properties in extrapolating extreme values and highlights the limitations of extremal limit theorems in certain distributions.