This function implements the automated proposal from Section 2.2 of Langousis et al. (2016) for mean residual life plots. It returns the threshold that minimize the weighted mean square error and moment estimators for the scale and shape parameter based on weighted least squares.
thselect.mrl(xdat, thresh, kmax, plot = TRUE, ...)a list containing
thresh: candidate threshold vector
thresh0: selected threshold
scale: scale parameter estimate
shape: shape parameter estimate
mrl: empirical mean excess values
xdat: ordered observations
intercept: intercept for mean excess value at chosen threshold
slope: slope for mean excess value at chosen threshold
tmanual: logical; TRUE if the user passed a vector of thresholds
[numeric] vector of observations
[numeric] vector of thresholds; if missing, uses all order statistics from the 20th largest until kmax as candidates
[integer] maximum number of order statistics
[logical] if TRUE (default), return a plot of the mean residual life plot with the fitted slope
and the chosen threshold
additional arguments, currently ignored
The procedure consists in estimating the usual mean residual life as a function of the threshold, and looking for an order statistic or threshold value above which the fit is more or less linear.
Langousis, A., A. Mamalakis, M. Puliga and R. Deidda (2016). Threshold detection for the generalized Pareto distribution: Review of representative methods and application to the NOAA NCDC daily rainfall database, Water Resources Research, 52, 2659--2681.