Hydrological Frequency Analysis: Some Results on Discriminating between the Gumbel or Weibull Probability Distributions and Other Competing Models

摘要

The Gumbel and Weibull distributions are closely related probability models with many hydro logical and environmental applications. Quite often, when trying to select between one of these distributions and a competing model to fit a data set, the commonly used goodness of fit tests lead to the rejection of neither of the competing models, but the user still needs an objective means of selecting between them. We compare three discrimination methods between the Gumbel/Weibull model and alternative models with the same number of unknown parameters. We base the comparison on the methods' discrimination power and discrimination bias. One method is the classical ratio of maximized likelihood (RML) procedure. When the competing models have the same number of unknown parameters, RML is equivalent to using the Akaike information criterion (AIC) or the Bayesian information criterion (BIC). Another method is TN.SW, which employs a transformation of the sample to normality, followed by an application of the Shapiro-Wilk (SW) statistic for testing normality. A third method, TN.PPCC, uses the same idea as TN.SW but is based on the probability plot correlation coefficient (PPCC) statistic. We conclude that TN.SW has advantages that merit further follow-up in future research. We illustrate our obtained results in an application involving frequency analysis of low river flows.