Given a sample of observations, calculate the L-skewness and L-kurtosis over a set of candidate thresholds. For each threshold candidate, we find the L-skewness that minimizes the sum of squared distance between the theoretical L-skewness and L-kurtosis of the generalized Pareto distribution, $$\min_{\tau_3} (t_3-\tau_3)^2 + [t_4 - \tau_3(1+5\tau_3)/(5+\tau_3)]^2.$$ The function returns the threshold with the minimum distance.
Arguments
- xdat
[numeric] vector of observations
- thresh
[numeric] vector of candidate thresholds. If missing, 20 sample quantiles starting at the 0.25 quantile in increments of 3.75 percent.
- plot
[logical] if
TRUE, return a plot of the sample L-kurtosis against the L-skewness, along with the theoretical generalized Pareto curve.
References
Silva Lomba, J., Fraga Alves, M.I. (2020). L-moments for automatic threshold selection in extreme value analysis. Stoch Environ Res Risk Assess, 34, 465–491. doi:10.1007/s00477-020-01789-x