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

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−Probability plotQQ−plotModel0.0 0.4 0.8−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− − −− − − −●●● ●●●●●●●●●●●●● ● ●●●●●●●● ●● ●●●●●●●●●●●● ●● ●●●●●●●●●● ● ●●●●●Empirical10 20 30 40−●● ● ●●●●● ●●●●● ●−−−−−−−−−−− − − −−−−− −−−−−●0.0 0.2 0.4 0.6 0.8 1.05 10 15 20 25 30EmpiricalModelDensity PlotReturn Level Plot●Density0.00 0.10 0.20Return Level5 15 25 35● ● ●●● ●●●●●●● ● ● ●●10 20 30 40 50Quantile0.5 2.0 5.0 20.0 100.0Return Period (Years)Figure 12: Graphic diagnostics for river Ardières at Beaujeu26
The result of function fitgpd gives the name of the estimator, if a varying threshold was used, thethreshold value, the number and the proportion of observations above the threshold, parameter estimates,standard error estimates and type, the asymptotic variance-covariance matrix and convergence diagnostic.Figure 12 shows graphic diagnostics for the fitted model. It can be seen that the fitted model “mle” seemsto be appropriate. Suppose we want to know the return level associated to the 100-year return period.> rp2prob(retper = 100, npy = npy)npy retper prob1 1.707897 100 0.9941448> prob qgpd(prob, loc = 6, scale = mle$param["scale"], shape = mle$param["shape"])scale36.44331To take into account uncertainties, Figure 13 depicts the profile confidence interval for the quantileassociated to the 100-year return period.> gpd.pfrl(mle, prob, range = c(25, 100), nrang = 200)If there is some troubles try to put vert.lines = FALSE or changethe range...conf.inf conf.sup25.56533 90.76633Sometimes it is necessary to know the estimated return period of a specified events. Lets do it with thelarger events in “events1”.> maxEvent maxEvent[1] 44.2> prob probshape0.9974115> prob2rp(prob, npy = npy)npy retper prob1 1.707897 226.1982 0.9974115Thus, the largest events that occurs in June 2000 has approximately a return period of 240 years.Maybe it is a good idea to fit the GPD with the other estimators available in the POT package.3 As the asymptotic approximation by a GPD is not accurate anymore.27
Page 3 and 4: z ≤ 0, Coles et al. (1999) use th
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
Page 25: timeobsMin. :1970 Min. : 0.0221st Q
Page 29 and 30: ADependence Models for Bivariate Ex
Page 31: Liang Peng and A.H. Welsh. Robust e

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