Assessment of an L-kurtosis-based criterion for quantile estimation

The estimation of extreme quantiles corresponding to small probabilities of exceedance is commonly required in the risk analysis of flood protection s tructures. The usefulness of L-moments has been Well recognized in the stat istical analysis of data, because they can be estimated with less uncertain ty than that associated with traditional moment estimates. The objective of the paper is to assess the effectiveness of L-kurtosis in the method of L- moments for distribution fitting and quantile estimation from small samples . For this purpose, the performance of the proposed L-kurtosis-based criter ion is compared against a set of benchmark measures of goodness of fit, nam ely, divergence, integrated-square error, chi square, and probability-plot correlation, The divergence is a comprehensive measure of probabilistic dis tance used in the modem information theory for signal analysis and pattern recognition. Simulation results indicate that the L-kurtosis criterion can provide quantile estimates that are in good agreement with benchmark estima tes obtained from other robust criteria. The remarkable simplicity of the c omputation makes the L-kurtosis criterion an attractive tool for distributi on selection.