extreme value theory: part ii sample (n=1000) from a normal distribution n(0,1) and fitted curve
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Extreme Value Theory: Part II
Sample (N=1000) from a Normal Distribution N(0,1) and fitted curve
Two main kind of Models: Block-maxima and Threshold approaches
Parameter Estimation for GEV Block Maxima
Parameter estimates:
Let:
Maximum likelihood method:
Then:
GEV: Graphical Model Checks
• Probability plot:
• Quantile plots:
• Return level plot:
Return level estimation for high quantiles:
• Profile log-likelihood function:
Example Malawi (Chitedze)
Daily rainfall Seasonal Maxima
MLE parameter estimates
Profile log-likelihood for 100 year return level:
Estimators include:
• Pickands estimator
• Hill‘s estimator
• Deckers-Einmahl-de Haan estimator
Parameter Estimation for GEV Block Maxima
Parameter Estimation II for GEV:
Threshold Models:
Asymptotic model approach:
Threshold models:
Threshold models: Generalized Pareto Distribution
Threshold models: Generalized Pareto Distribution
Threshold selection
Mean residual life plot
Parameter Estimation: Maximum likelihood
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.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