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Modeling Extreme Events

 Code 15636 Year 1 Semester S2 ECTS Credits 6 Workload TP(45H) Scientific area Mathematics Entry requirements Does not have. Learning outcomes To know the relevant properties of order statistics and understand the diversity of possible applications in probabilistic and statistical modeling.To understand, to relate and to apply probabilistic and statistical concepts and methods of Extreme Value Theory.Apply proper mathematical techniques in the analysis of extreme values in situations of interest. Syllabus 1- Introduction to Extreme Value Theory (EVT)Why is EVT important?Examples of Applications2 – Exact Distributions of Order StatisticsDistribution of a Single Order StatisticJoint Distribution of Two or more Order statisticsDistribution of some systematic statistics: sample range and sample quasi-range3- Asymptotic distributions of Extreme Order StatisticsExtremal Types TheoremKhintchine’s Convergence TheoremMax-stabilityGeneralized Extreme Value Distribution (GEV)Max-domains of attractionPoisson Properties of exceedancesParameters of rare events: Extreme Value Index; Extremal Index; Return Period of a High Threshold; Value-at-Risk and Tail Probability4 – Estimating the parameters of rare events under a parametric approachAnnual maximum methodMaximum likelihood estimators for the parameters of the GEV distributionProbability weighted moments estimators for the parameters of the GEV distributionEstimating other interesting parameters in EVT5 - Case Studies Main Bibliography Coles, S. (2001). An introduction to statistical modeling of extreme values. New York: Springer.Beirlant, J., Goegebeur, Y., Segers, J., Teugels, J.L., Waal, D. (2005). Statistics of extremes: theory and applications.Hoboken: John Wiley.Reiss, R.-D. (2007). Statistical analysis of extreme values: with applications to insurance, finance, hydrology and other fields. 3rd ed. Basel: Birkhäuser.Gumbel, E.J. (2004). Statistics of extremes. Mineola: Dover Publications.de Haan, L., Ferreira, A. (2006). Extreme value theory: an introduction. New York: Springer.Gomes, I., Fraga Alves, I., Ribeiro, C. (2013). Análise de Valores Extremos: Uma introdução. XXI Congresso da Sociedade Portuguesa de Estatística. Edições SPE. Language Portuguese. Tutorial support is available in English.

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Mathematics and Applications
Last updated on: 2023-06-12

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