Assessment of an L-Kurtosis-Based Criterionfor Quantile Estimation

Abstract

The estimation of extreme quantiles corresponding to small probabilities of exceedance is commonly required in the risk analysis of flood protection structures. The usefulness of L-moments has been well recognized in the statistical analysis of data, because they can be estimated with less uncertainty 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 criterion is compared against a set of benchmark measures of goodness of fit, namely, divergence, integrated-square error, chi square, and probability-plot correlation. The divergence is a comprehensive measure of probabilistic distance used in the modern 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 estimates obtained from other robust criteria. The remarkable simplicity of the computation makes the L-kurtosis criterion an attractive tool for distribution selection.