Discriminating between the Lognormal and the Log-Logistic Distributions for Hydrological Frequency Analysis

Discriminating between competitive statistical models is an important problem in hydrological frequency analysis. The present study deals with discrimination between the two-parameter lognormal (LN2) and the two-parameter log-logistic (LLOG2) distributions, or, equivalently, between the normal (N) and the logistic (LOG) distributions. Previous work using the likelihood ratio (LR) statistic suggested that discrimination between these distributions is difficult, and that criteria other than LR need to be studied in hope of finding criteria with better discriminating power. In the present study, several criteria other than LR are considered, and their ability to discriminate between the LN2 and LLOG2 distributions is assessed using Monte Carlo simulation. The results confirm previous findings that discrimination between the two distributions is difficult with small samples, but a criterion based on the Shapiro-Wilk statistic appears to be the most appropriate for sample sizes typically encountered in hydrology. Two hydrological examples are presented to illustrate how obtained results can be implemented in practice.