Simulation in Extreme-Value Estimation by a Combined S-PLUS and C-Program

Extreme-value estimation is of great importance when one is interested in e.g. protecting land against sea by dikes. In Dekkers [1] asymptotic theory for some estimates for the extreme-value index, estimates for very large quantiles (outside the sample range) are studied as well as estimators for the right endpoint of a distribution function in case this endpoint is finite.In order to obtain some insight in the behaviour of these estimates for finite samples, some simulation studies are carried out and comparisons between the asymptotic theory and the simulation results are made. The statistical package S-PLUS [2,3] is used for the simulation and the further analysis in combination with a C-program. This combination is the main object of this paper, but first some theoretical results are given.