GEV_shape_plot function

Fitted GEV Shape as a Function of the Threshold

Fit GEVs to block maxima and plot the fitted GPD shape as a function of the block size.

GEV_shape_plot(x, blocksize = tail(pretty(seq_len(length(x)/20), n = 64), -1),
               estimate.cov = TRUE, conf.level = 0.95,
               CI.col = adjustcolor(1, alpha.f = 0.2),
               lines.args = list(), xlim = NULL, ylim = NULL,
               xlab = "Block size",  ylab = NULL,
               xlab2 = "Number of blocks", plot = TRUE, ...)

Arguments

• x: vector of numeric data.
• blocksize: numeric vector of block sizes for which to fit a GEV to the block maxima.
• 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 block size.
• 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 block sizes considered, the corresponding block maxima and the fitted GEV distribution objects as returned by the underlying fit_GEV_MLE().

Details

Such plots can be used in the block maxima method for determining the optimal block size (as the smallest after which the plot is (roughly) stable).

Author(s)

Marius Hofert

Examples

set.seed(271)
X <- rPar(5e4, shape = 4)
GEV_shape_plot(X)
abline(h = 1/4, lty = 3) # theoretical xi = 1/shape for Pareto