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Last Updated: 2026-02-05 15:09:58
Abstract
This course yields a mathematical introduction into the theory of extremes. Besides a derivationof the Fisher-Tippett theorem for sample maxima, it is also shown how the theory of point pro-cesses yields a methodological basis for the Peaks Over Threshold method. Some examplesof statistical data analysis for the modelling of extremes will also be discussed.
Objective
This course yields a mathematical introduction into the theory of extremes. Besides a derivation of the Fisher-Tippett theorem for sample maxima, it is also shown how the theory of point pro- cesses yields a methodological basis for the Peaks Over Threshold method. Some examples of statistical data analysis for the modelling of extremes will also be discussed.
Content
- The Fisher-Tippett Theorem - The Method of Block Maxima - The Maximal Domain of Attraction - The Frechet, Gumbel and Weibull distributions - Regular Variation -The POT method - The Point Process Method -The Pickands-Balkema-de Haan Theorem and its applications
Resources
Literature
P.Embrechts, C.Klueppelberg and T.Mikosch (1997) The Modelling of Extremal Events in Insurance and Finance. Springer. S.I. Resnick (1987) Extreme Values, Regular Variation and Point Processes. Springer.
General Information
- Language
- English
Examination
- Type
- session examination
- Mode
- oral 20 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture | Extreme Value Theory |
|
2 h weekly |