A comparison of tail probability estimators for flood frequency analysis

Selected techniques for estimating exceedance frequencies of annual maximum flood events at a gaged site are compared in this paper. Four tail probability estimators proposed by Hill (PT1), Hosking and Wallis (PT2) and by Breiman and Stone (ET and QT), and a variable kernel distribution function estimator (VK-C-AC) were compared for three situations - Gaussian data, skewed data (three-parameter gamma) and Gaussian mixture data. The performance of these estimators was compared with method of moment estimates of tail probabilities, using the Gaussian, Pearson Type III, and extreme value distributions. Since the results of the tail probability estimators (PT1, PT2, ET, QT) varied according to the situation, it is not easy to say which tail probability estimator is the best. However, the performance of the variable kernel estimator was relatively consistent across the estimation situations considered in terms of bias and r.m.s.e.