Estimation of probability tails based on generalized extreme value distributions

For high reliability devices or structures it is not uncommon that the probabilities to be estimated are lower than 10-6. In such cases the standard methods of the empirical fit approach and the counting approach may become impractical. In this paper the estimation problem is handled by extrapolation methods which give an approximate expression of an entire probability tail on the basis of the classical and generalized Extreme Value Theory. Comparative performance of these methods, with respect to the classical ones, are drawn be means of a simulation study, which has taken into account the effect of the sample size, the population being investigated and the estimation method.