A bivariate extension of the Hosking and Wallis goodness-of-fit measure for regional distributions

This study presents a bivariate extension of the goodness-of-fit measure for regional frequency distributions developed by Hosking and Wallis [1993] for use with the method of L-moments. Utilising the approximate joint normal distribution of the regional L-skewness and L-kurtosis, a graphical representation of the confidence region on the L-moment diagram can be constructed as an ellipsoid. Candidate distributions can then be accepted where the corresponding theoretical relationship between the L-skewness and L-kurtosis intersects the confidence region, and the chosen distribution would be the one that minimises the Mahalanobis distance measure. Based on a set of Monte Carlo simulations it is demonstrated that the new bivariate measure generally selects the true population distribution more frequently than the original method. Results are presented to show that the new measure remains robust when applied to regions where the level of inter-site correlation is at a level found in real world regions. Finally the method is applied to two different case studies involving annual maximum peak flow data from Italian and British catchments to identify suitable regional frequency distributions.