'n Ondersoek na die eindige steekproefgedrag van inferensiemetodes in ekstreemwaarde-teorie

Extremes are unusual or rare events. However, when such events – for exampleearthquakes, tidal waves and market crashes - do take place, they typically causeenormous losses, both in terms of human lives and monetary value. For this reason,it is of critical importance to accurately model extremal events. Extreme value theoryentails the development of statistical models and techniques in order to describe andmodel such rare observations.In this document we discuss aspects of extreme value theory. This theory consists oftwo approaches: The classical maxima method, based on the properties of themaximum of a sample and the more popular threshold theory, based upon theproperties of exceedances of a specified threshold value. This document providesthe practitioner with the theoretical and practical tools for both these approaches.This will enable him/her to perform extreme value analyses with confidence.Extreme value theory – for both approaches - is based upon asymptotic arguments.For finite samples, the limiting result for the sample maximum holds approximatelyonly. Similarly, for finite choices of the threshold, the limiting distribution forexceedances of that threshold holds only approximately. In this document weinvestigate the quality of extreme value based inferences with regard to the unknownunderlying distribution when the sample size or threshold is finite. Estimation ofextreme tail quantiles of the underlying distribution, as well as the calculation ofconfidence intervals, are typically the most important objectives of an extremeanalysis. For that reason, we evaluate the accuracy of extreme based inferences interms of these estimates. This investigation was carried out using a simulation study,performed with the software package S-Plus.