Comparison of four methods to select the best probability distribution for frequency analysis of annual maximum precipitation using Monte Carlo simulations

Hydrologic design requires estimation of extreme hydrological events, whose magnitude and probability are estimated using a probability distribution function (PDF). Since estimations can vary considerably depending on the PDF that is used, the selection of an appropriate PDF is essential. This study compares the performance of four different methods for selecting probability distributions analyzing 56 data series of annual maximum precipitation in Mexico: the Akaike Information Criterion (AIC), the Bayesian Information Criterion (BIC), the Kolmogorov-Smirnov (KS) test, and the standard error of fit (SEF) statistic. Comparison of these methods was done by means of Monte Carlo simulations, in which data were generated from a mother distribution, and the ability of the different selection procedures to choose the right distribution was observed. Several different simulation scenarios were analyzed, varying the mother distribution and the sample size. None of the selection criteria proved to be superior to the others in all cases. AIC and BIC performed better when the mother distribution had two parameters, while the KS and SEF performed better when the mother distribution had three parameters. It was observed that the SEF and KS tend to select three- parameter distributions even when a third parameter is not justified, whereas the AIC and BIC tend to penalize excessively the addition of a third parameter, even when it is necessary.