GEV_shape_plot: Fitted GEV Shape as a Function of the Threshold

In qrmtools: Tools for Quantitative Risk Management

Fitted GEV Shape as a Function of the Threshold

Description

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

Usage

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().

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).

Value

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().

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

qrmtools documentation built on July 24, 2025, 3:02 a.m.