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Introduction to extreme-value analysis - WMM9AMXX

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  • Number of hours

    • Lectures : -
    • Tutorials : -
    • Laboratory works : -
    • Projects : -
    • Internship : -
    • Written tests : -
    ECTS : 0.0
  • Officials : Stephane GIRARD

Goals

This lecture introduces probabilistic concepts and associated statistical methods in extreme-value analysis and tail modelling.

Content

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.

Prerequisites

Knowledge of statistics and probability will be assumed.

Tests

3 hour written exam

Calendar

The course exists in the following branches:

  • Curriculum - Master 2 in Applied Mathematics - Semester 9
see the course schedule for 2020-2021

Additional Information

Course ID : WMM9AMXX
Course language(s): FR

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.

https://sites.google.com/view/ow-extremes/

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Date of update June 30, 2020

Université Grenoble Alpes