Number of hours
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ECTS
ECTS 0.0
Goal(s)
This lecture introduces probabilistic concepts and associated statistical methods in extreme-value analysis and tail modelling.
Responsible(s)
Stephane GIRARD
Content(s)
Taking into account extreme events (heavy rainfalls, floods, etc.) is often crucial in the statistical approach to risk modeling. In this context, the behavior of the distribution tail is then more important than the shape of the central part of the distribution. Extreme-value theory offers a wide range of tools for modeling and estimating the probability of extreme events.
In particular, the following points will be addressed in the course:
1) Asymptotic behavior of the largest value of a sample. Extreme-value Distribution (EVD). Maximum domains of attraction (Fréchet, Weibull and Gumbel). Asymptotic behavior of excesses over a threshold. Generalized Pareto Distribution (GPD). Regularly varying functions.
2) Estimation of the parameters of the EVD and GPD. Hill estimator. Application to the estimation of extreme quantiles. Illustration on simulated and real data.
PrerequisitesKnowledge of statistics and probability will be assumed.
Test
3 hour written exam
Calendar
The course exists in the following branches:
- Curriculum - Master 2 in Applied Mathematics - Semester 9
Additional Information
Course ID : WMM9AMXX
Course language(s): 
You can find this course among all other courses.
Bibliography
Stuart G. Coles. An Introduction to Statistical Modeling of Extreme Values. Springer Series in Statistics. London, 2001.