An R Package for Univariate and Bivariate Peaks Over Threshold ...
An R Package for Univariate and Bivariate Peaks Over Threshold ...
An R Package for Univariate and Bivariate Peaks Over Threshold ...
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Estimator: MLEDeviance: -173.0829AIC: -169.0829Varying <strong>Threshold</strong>: TRUE<strong>Threshold</strong> Call: 1:2Number Above: 500Proportion Above: 1Estimatesscale shape0.29079 0.06207St<strong>and</strong>ard Error Type: observedSt<strong>and</strong>ard Errorsscale shape0.01934 0.04929Asymptotic Variance Covariancescale shapescale 0.0003739 -0.0006681shape -0.0006681 0.0024297Optimization In<strong>for</strong>mationConvergence: successfulFunction Evaluations: 43Gradient Evaluations: 12Note that the varying threshold is repeated cyclically until it matches the length of object x.3.3.2 The bivariate caseThe generic function to fit bivariate POT is fitbvgpd. There is currently 6 models <strong>for</strong> the bivariateGPD - see <strong>An</strong>nexe A. All of these models are fitted using maximum likelihood estimator. Moreover, theapproach uses censored likelihood - see (Smith et al., 1997).> x y Mlog MlogCall: fitbvgpd(data = cbind(x, y), threshold = c(0, 2), model = "log")Estimator: MLEDependence Model <strong>and</strong> Strenght:Model : Logisticlim_u Pr[ X_1 > u | X_2 > u] = 0.005Deviance: 1374.676AIC: 1384.676Marginal <strong>Threshold</strong>: 0 2Marginal Number Above: 500 500Marginal Proportion Above: 1 1Joint Number Above: 500Joint Proportion Above: 1Number of events such as {Y1 > u1} U {Y2 > u2}: 50013
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