1. Extreme Value Theory: Part I
Sample (N=1000) from a Normal Distribution N(0,1) and fitted curve

2. Two main kind of Models: Block-maxima and Threshold approaches

3. Asymptotics: Problems of degenerate distributions

4. Asymptotic models for Maxima I:

5. Example: Densities

6. Densities of distribution:
Frechet
Weibull
Gumbel

7. Important relationship:

8. Asymptotic models for Maxima II:
From Fisher Tippet theorem:

9. Class of non-degenerate limit distributions of maxima:
Example: Standard exponential distribution
In other words, a distribution is max-stable if, and only if, it is a generalized
extreme value distribution.

10. Maximum Domain of Attraction:
Example: Standard exponential distribution

11. Example: Uniform distribution

12. End of Part I of Extreme Value Theory