Comparative performance analysis of some extrapolative estimators of probability tails

In some applications, estimation of probabilities of the order of 10-6 or lower is required. Extrapolative methods based on extreme value theory (EVT) and generalized extreme value theory (GEVT) are considered. They give a closed-form approximation of the probability tail in terms of two or three parameters, respectively. A Monte Carlo simulation study was carried out to assess EVT and GEVT estimators' performances with respect to several factors, such as estimation methods, initial distribution, sample size, and partition of the initial sample. It was found that the GEVT estimators are consistently more efficient, while achieving a substantial sample-size saving with respect to the conventional counting procedure. Some applications to estimation problems encountered in radar systems design are considered.