Threshold stability plots for left-truncated Hill estimators

Given a vector of exceedances and some potential choices of \(k\) for the threshold, compute the left-truncated Hill estimators for each value of k and use these to compute the variance and slope of the estimator

Usage

tstab.lthill(xdat, k, which = c("lthill", "var", "slope"), log = TRUE, ...)

Arguments

xdat: [numeric] vector of positive observations
k: [integer] number of order statistics for the threshold
which: [string] the type of plot, showing the left-truncated Hill plot on the log, the log of the variance of the estimator, or the log slope
log: [logical] if TRUE (default), shows the Hill plot on the log-scale
...: additional parameters for color, etc. to be passed to plot

Value

an invisible list with lthill, order statistics, the log variance and the log scale.

References

Bladt, M., Albrecher, H. & Beirlant, J. (2020) Threshold selection and trimming in extremes. Extremes, 23, 629-665 . doi:10.1007/s10687-020-00385-0

Examples

xdat <- 10/(1 - runif(n = 1000)) - 10
tstab.lthill(xdat = xdat, k = c(50,100,200))