An R Package for Univariate and Bivariate Peaks Over Threshold ...

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If there is some troubles try to put vert.lines = FALSE or changethe range...conf.inf conf.sup25.56533 90.76633Profile Log−likelihood−143.5 −143.0 −142.5 −142.0 −141.540 60 80 100Return LevelFigure 13: Profile-likelihood function for the 100-year return period quantile28
ADependence Models for Bivariate Extreme Value DistributionsA.1 The Logisitic modelThe logisitic model is defined by:V (x, y) =(x −1/α + y −1/α) α, 0 < α ≤ 1 (A.1)Independence is obtained when α = 1 while total dependence for α → 0.The Pickands’ dependence function for the logistic model is:A : [0, 1] −→ [0, 1][w ↦−→ (1 − w) 1 α+ w 1 α] αA.2 The Asymetric Logistic modelThe asymetric logistic model is defined by:with 0 < α ≤ 1, 0 ≤ θ 1 , θ 2 ≤ 1.V (x, y) = 1 − θ 1x+ 1 − θ 2y[ ( ) − 1 ( ) xα − 1] αyα++ ,θ 1 θ 2Independence is obtained when either α = 1, θ 1 = 0 or θ 2 = 0. Differents limits occur when θ 1 and θ 2are fixed and α = 1 → 0.The Pickands’ dependence function for the asymetric logistic model is:A(w) = (1 − θ 1 ) (1 − w) + (1 − θ 2 ) w +[(1 − w) 1 1α θα1 + w 1 1α θα2] αA.3 The Negative Logistic modelThe negative logistic model is defined by:V (x, y) = 1 x + 1 y − (xα + y α ) − 1 α, α > 0 (A.2)Independence is obtained when α → 0 while total dependence when α → +∞.The Pickands’ dependence function for the negative logistic model is:A(w) = 1 − [ (1 − w) −α + w −α] − 1 αA.4 The Asymetric Negative Logistic modelThe asymetric negative logistic model is defined by:V (x, y) = 1 x + 1 [( ) α ( ) α ] − 1x yαy − +, α > 0, 0 < θ 1 , θ 2 ≤ 1θ 1 θ 2Independence is obtained when either α → 0, θ 1 → 0 or θ 2 → 0. Different limits occur when θ 1 and θ 2are fixed and α → +∞.The Pickands’ dependence function for the asymetric negative logistic model is:[ (1 ) −α ( ) ] −α − 1α− w wA(w) = 1 −+θ 1 θ 229
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Page 5 and 6: 3.2 Threshold SelectionThe location
Page 7 and 8: Mean Residual Life PlotMean Excess0
Page 9 and 10: ●●●L−Moments Plotτ 40.0 0.
Page 11 and 12: 3.3 Fitting the GPD3.3.1 The univar
Page 13 and 14: Estimator: MLEDeviance: -173.0829AI
Page 15 and 16: Pickands' Dependence FunctionA (x)0
Page 17 and 18: 3.4 Confidence IntervalsOnce a stat
Page 19 and 20: conf.inf conf.sup7.220334 10.219962
Page 21 and 22: ˆ which = 4 for a return level plo
Page 23 and 24: obs0 10 20 30 401970 1975 1980 1985
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Page 27: The result of function fitgpd gives
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