Problems in the extreme value analysis

Engineering design for structural safety is largely based on the statistics of natural hazards. These statistics are utilized by applying the theory of extremes, which predicts a cumulative distribution function of the extreme events. The parameters of this distribution are found by a fit to the historical extremes and the probabilities of potentially disastrous events are then calculated. It is pointed out here that this procedure often results in underestimation of the risk. This is because wrong probability plotting positions are widely used and because theoretical extreme value distributions are asymptotic only, so that in many cases they bring misleading information to the analysis. The means to avoid these problems in the extreme value analysis are outlined.