# 401-3919-60L  An Introduction to the Modelling of Extremes

 Semester Frühjahrssemester 2014 Dozierende P. Embrechts Periodizität jährlich wiederkehrende Veranstaltung Lehrsprache Englisch

 Kurzbeschreibung This course yields an introduction into the one-dimensional theory of extremes, and this both from a probabilistic as well as statistical point of view. This course can be seen as a first course on extremes, a sequel concentrating more on multivariate extremes. Lernziel In this course, students learn to distinguish between so-called normal models, i.e. models based on the normal or Gaussian distribution, and so-called heavy-tailed or power-tail models. They learn to do some standard modelling and data analysis for one-dimensional data. The probabilistic key theorems are the Fisher-Tipett Theorem and the Balkema-de Haan-Pickands Theorem. These lead to the statistical techniques for the analysis of extremes or rare events known as the Block Method, and Peaks Over Threshold method, respectively. Inhalt - Introduction to rare or extreme events- Regular Variation- The Convergence to Types Theorem- The Fisher-Tippett Theorem- The Method of Block Maxima- The Maximal Domain of Attraction- The Fre'chet, Gumbel and Weibull distributions- The POT method- The Point Process Method: a first introduction- The Pickands-Balkema-de Haan Theorem and its applications- Some extensions and outlook Skript There will be no script available. Literatur At a more elementary level:[1] S.G. Coles (2001) An Introduction to Statistical Modeling of Extreme Values. Springer.[2] R.-D. Reiss and M. Thomas (1997) Statistical Analyis of Extreme Values. Birkhaeuser.At an intermediate level:[3] J. Beirlant, Y. Goegebeur, J. Segers and J.L. Teugels (2004) Statistics of Extremes: Theory and Applications, Wiley. [4] P. Embrechts, C. Klueppelberg and T. Mikosch (1997) Modelling Extremal Events for Insurance and Finance. Springer.[5] S. I. Resnick (2007) Heavy-Tail Phenomena. Probabilistic and Statistical Modeling. Springer. At a more advanced level:[6] L. de Haan and A. Ferreira (2006) Extreme Value Theory. An Introduction. Springer.[7] S. I. Resnick (1987) Extreme Values, Regular Variation, and Point Processes. Springer.