Introduction to extreme-value analysis
3 ECTS, C. 18h
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:
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.
Estimation of the parameters of the EVD and GPD. Hill estimator. Application to the estimation of extreme quantiles. Illustration on simulated and real data.
Knowledge of statistics and probability will be assumed.