Two-parameter probability distributions are among those frequently employed in hydrological frequency modeling, especially in the peaks-over-threshold approach to analysing hydrological extremes. When the practitioner fits several candidate models to a data set, selection of the final fitting model often reduces to having to pick, or "discriminate," between one specific pair of competitive models. We will review some widely used discrimination statistics (DS) in terms of their ability for correct selection between pairs of competitive 2-parameter models. We will also attempt to classify model pairs according to the difficulty to discriminate between them. Research has shown three DS to be among those most capable of correctly selecting between pairs of 2-parameter models. These DS are: (1) the ratio of maximized likelihood statistic-RML (closely associated with the Akaike Information Criterion-AIC and the Bayesian Information Criterion-BIC), (2) the Anderson-Darling (AD) goodness-of-fit (GoF) statistic, and (3) a (relatively new) DS derived from the Shapiro-Wilk GoF statistic, which we will denote by "TN.SW." Research has shown the TN.SW DS to be advantageous when applied to samples of size typically encountered in hydrology. A hydrological example will show the use of this DS in practice.
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