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Modeling Extreme Events

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 Applications 2 – Exact Distributions of Order Statistics Distribution of a Single Order Statistic Joint Distribution of Two or more Order statistics Distribution of some systematic statistics: sample range and sample quasi-range 3- Asymptotic distributions of Extreme Order Statistics Extremal Types Theorem Khintchine’s Convergence Theorem Max-stability Generalized Extreme Value Distribution (GEV) Max-domains of attraction Poisson Properties of exceedances Parameters of rare events: Extreme Value Index; Extremal Index; Return Period of a High Threshold; Value-at-Risk and Tail Probability 4 – Estimating the parameters of rare events under a parametric approach Annual maximum method Maximum likelihood estimators for the parameters of the GEV distribution Probability weighted moments estimators for the parameters of the GEV distribution Estimating other interesting parameters in EVT 5 - 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.