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

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Dispersion Index PlotDispersion Index0.8 1.0 1.2 1.4 1.6 1.85 10 15 20ThresholdFigure 4: The threshold selection using the diplot function10
3.3 Fitting the GPD3.3.1 The univariate caseThe main function to fit the GPD is called fitgpd. This is a generic function which can fit the GPDaccording several estimators. There are currently 17 estimators available: method of moments moments,maximum likelihood mle, biased and unbiased probability weighted moments pwmb, pwmu, mean powerdensity divergence mdpd, median med, pickands’ pickands, maximum penalized likelihood mple and maximumgoodness-of-fit mgf estimators. For the mgf estimator, the user has to select which goodness-of-fitstatistics must be used. These statistics are the Kolmogorov-Smirnov, Cramer von Mises, AndersonDarling and modified Anderson Darling. See the html help page of the fitgpd function to see all ofthem. Details for these estimators can be found in (Coles, 2001), (Hosking and Wallis, 1987), (Juárezand Schucany, 2004), (Peng and Welsh, 2001) and (Pickands, 1975).The MLE is a particular case as it is the only one which allows varying threshold. Moreover, two typesof standard errors are available: “expected” or “observed” information of Fisher. The option obs.fishspecifies if we want observed (obs.fish = TRUE) or expected (obs.fish = FALSE).As Pickands’ estimator is not always feasible, user must check the message of feasibility return by functionfitgpd.We give here several didactic examples.> x mom mle pwmu pwmb pickands med mdpd mple ad2r print(rbind(mom, mle, pwmu, pwmb, pickands, med, mdpd, mple,+ ad2r))scale shapemom 1.7563811022 0.21890796mle 1.7669554034 0.21254750pwmu 1.7577270679 0.21830938pwmb 1.7670734558 0.21415289pickands 1.9398703365 0.09973551med 1.9837826885 0.05076009mdpd 1.7779268149 0.20440353mple 1.7825858914 0.20187921ad2r 0.0006977949 47.80717364The MLE, MPLE and MGF estimators allow to fix either the scale or the shape parameter. For example,if we want to fit a Exponential distribution, just do (with eventually a fixed scale parameter):> x fitgpd(x, thresh = 1, shape = 0, est = "mle")Estimator: MLEDeviance: 304.1777AIC: 306.1777Varying Threshold: FALSE11
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: ●●●L−Moments Plotτ 40.0 0.
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 and 26: timeobsMin. :1970 Min. : 0.0221st Q
Page 27 and 28: The result of function fitgpd gives
Page 29 and 30: ADependence Models for Bivariate Ex
Page 31: Liang Peng and A.H. Welsh. Robust e

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