Choice between competitive pairs of frequency models for use in hydrology: a review and some new results

Abstract

A group of statistical distributions useful in hydrological frequency modelling are two-parameter distributions with one scale and one shape parameter. Discriminating between pairs of models within this group is of practical interest. The main discrimination tests that have appeared in the literature are reviewed and a broad comparison is undertaken of their ability to correctly identify the distribution within the pair of distributions being studied. An attempt is also made to classify pairs of distributions according to the difficulty of discriminating between them. In addition, several tests are formulated and compared to discriminate between the Weibull and the log-logistic distributions. These tests are also applicable, with the same ability of correctly choosing between the logistic and the extreme value type 1 models (for minima or maxima). A Monte Carlo study identifies three test statistics as the most powerful for correctly selecting between these models: the ratio of maximized likelihood, Anderson-Darling and (modified) Shapiro-Wilk statistics. The third of these test statistics is specifically shown to be advantageous with small samples. A hydrological example shows how this test statistic is used in practice. © 2012 Copyright 2012 IAHS Press.