Extreme Value Theory: Maximum Distribution

This lecture delves into the theory of extreme values, focusing on the distribution of maximum values of independent and identically distributed random variables. The instructor explains the concept of rescaling and approximating unknown distributions to obtain non-degenerate limit distributions. The lecture covers the extremal types theorem, discussing the parameters that define the limiting distribution. It also explores different types of distributions based on shape parameters, such as the Fréchet and Gumbel distributions. The exceedance theorem is introduced as an alternative approach to modeling extremes, emphasizing the importance of threshold exceedances. The connection between the Generalized Pareto Distribution and the Generalized Extreme Value Distribution is highlighted, showcasing the flexibility and applicability of these models in analyzing extreme events.