1. Extreme Value Theory: Part II Sample (N=1000) from a Normal Distribution N(0,1) and fitted curve

2. Two main kind of Models: Block-maxima and Threshold approaches

3. Parameter Estimation for GEV Block Maxima Parameter estimates: Let: Maximum likelihood method: Then:

4. GEV: Graphical Model Checks Probability plot: Quantile plots: Return level plot: Return level estimation for high quantiles: Profile log-likelihood function:

5. Example Malawi (Chitedze) Daily rainfallSeasonal Maxima MLE parameter estimates

7. Profile log-likelihood for 100 year return level:

8. Estimators include: Pickands estimator Hill‘s estimator Deckers-Einmahl-de Haan estimator Parameter Estimation for GEV Block Maxima

9. Parameter Estimation II for GEV:

11. Threshold Models:

12. Asymptotic model approach:

13. Threshold models:

14. Threshold models: Generalized Pareto Distribution

16. Threshold selection Mean residual life plot

17. Parameter Estimation: Maximum likelihood

20. Statistical Software for EVT Analysis: Easiest to use Matlab: EVIM: A Software Package for Extreme Value Analysis by Gencay, Selcuk and Uluguelyagci Manual and Software: http://www.sfu.ca/~rgencay/evim.htmlhttp://www.sfu.ca/~rgencay/evim.html S-Plus and R: ismev: An Introduction to Statistical Modeling of Extreme Values Manual and Software: http://cran.r-project.org/web/packages/ismev/index.html Other software products can be found for example at: http://www.ral.ucar.edu/~ericg/softextreme.php http://www.isse.ucar.edu/extremevalues/extreme.html