An Introduction to Statistical Extreme Value Theory - IMAGe

More documents

Recommendations

Info

Threshold ModelsThe distribution of Y := X − u|X > u converges to(as u → ∞)H(y) = 1 − (1 + ξ ỹ σ )− 1 ξ .H(y) is called the “Generalized Pareto” distribution(GPD) with 2 parameters.shape parameter ξscale parameter ˜σ.The shape parameter ξ is the “same” parameter as in theGEV distribution.Tutorial in Extreme Value Theory
Fitting a GPD – Estimating ParametersUse the 184 exceedances over the threshold u = 80to fit the GEV distribution.Estimate the 2 parameters ξ and σ (using “maximumlikelihood” using statistical software (R).Get a GPD distribution with ξ = 0.22 and σ = 51.46.Density0.000 0.005 0.010 0.0150 50 100 150 200 250Tutorial 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 and 12: Fitting a GEV - Return LevelsOften
Page 13 and 14: Threshold ModelsModel exceedances o
Page 15: Threshold ModelsModel exceedances o
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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?