An Introduction to Statistical Extreme Value Theory - IMAGe

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Fitting a GEV – Return LevelsOften of interest: return level z mP (M > z m ) = 1 m .Expect every m th observation to exceed the level z m .Or: at any point, there is a 1/m% probability to exceedthe level z m .Can be computed easily once the parameters are“known”.E.g. m = 100, then z 100 = 420, i.e. expect the annualdaily maximum to exceed 4.2 inches every 100 yearsin Boulder.Tutorial in Extreme Value Theory
Fitting a GEV – Return LevelsOften of interest: return level z mP (M > z m ) = 1 m .Expect every m th observation to exceed the level z m .Return Levels for Boulderm year return level0 100 200 300 4000 20 40 60 80 100m (years)Tutorial in Extreme Value Theory
Page 1 and 2: An Introduction toStatistical Extre
Page 3 and 4: FundamentalsIn classical statistics
Page 5 and 6: FundamentalsIn extreme value theory
Page 7 and 8: Block Maxima ApproachModel extreme
Page 9: Fitting a GEV - Estimating Paramete
Page 13 and 14: Threshold ModelsModel exceedances o
Page 15 and 16: Threshold ModelsModel exceedances o
Page 17 and 18: Fitting a GPD - Estimating Paramete
Page 19 and 20: Fitting a GPD - Choosing a Threshol
Page 21 and 22: Fitting a GPD - Choosing a Threshol
Page 23 and 24: Uncertainty (GEV)Essentially, the m
Page 25 and 26: Uncertainty (GPD)More data means le
Page 27 and 28: Dependence - DeclusteringFor the GE
Page 29 and 30: Dependence - (fitting the GPD)Choos
Page 31 and 32: Dependence - (fitting the GPD)Modif
Page 33 and 34: Dependence - (fitting the GPD)Use u
Page 35 and 36: SeasonalityTo incorporate seasonali

An Introduction to Statistical Extreme Value Theory - IMAGe

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