An Introduction to Statistical Extreme Value Theory - IMAGe

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Fitting a GEV – AssumptionsWe did not need to know what the underlyingdistribution of each X i , i.e. the daily total rainfall was.Underlying assumption: observations are “iid”independently andidentically distributed.Tutorial in Extreme Value Theory
Threshold ModelsModel exceedances over a high threshold u –X − u|X > u.Daily total rainfall for Boulder exceeding 80 (1/100 in).Allows to make more efficient use of the data.Daily total rainfall for Boulder (1948−2001)max. daily precip in 1/100 in0 100 200 300 4001960 1970 1980 1990 2000yearsTutorial 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 and 10: Fitting a GEV - Estimating Paramete
Page 11: Fitting a GEV - Return LevelsOften
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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