GPD_shape_plot function

Fitted GPD Shape as a Function of the Threshold

Fit GPDs to various thresholds and plot the fitted GPD shape as a function of the threshold.

GPD_shape_plot(x, thresholds = seq(quantile(x, 0.5), quantile(x, 0.99),
                                   length.out = 65),
               estimate.cov = TRUE, conf.level = 0.95,
               CI.col = adjustcolor(1, alpha.f = 0.2),
               lines.args = list(), xlim = NULL, ylim = NULL,
               xlab = "Threshold", ylab = NULL,
               xlab2 = "Excesses", plot = TRUE, ...)

Arguments

• x: vector of numeric data.
• thresholds: numeric vector of thresholds for which to fit a GPD to the excesses.
• estimate.cov: logical indicating whether confidence intervals are to be computed.
• conf.level: confidence level of the confidence intervals if estimate.cov.
• CI.col: color of the pointwise asymptotic confidence intervals (CIs); if NA, no CIs are shown.
• lines.args: list of arguments passed to the underlying lines() for drawing the shape parameter as a function of the threshold.
• xlim, ylim, xlab, ylab: see plot().
• xlab2: label of the secondary x-axis.
• plot: logical indicating whether a plot is produced.
• ...: additional arguments passed to the underlying plot().

Returns

Invisibly returns a list containing the thresholds considered, the corresponding excesses and the fitted GPD objects as returned by the underlying fit_GPD_MLE().

Details

Such plots can be used in the peaks-over-threshold method for determining the optimal threshold (as the smallest after which the plot is (roughly) stable).

Author(s)

Marius Hofert

Examples

set.seed(271)
X <- rt(1000, df = 3.5)
GPD_shape_plot(X)