Two kinds of moment ratio diagrams and their applications in hydrology

We refocus attention on moment ratio diagrams and their uses in hydrology with four major objectives: (1) to summarize the information available in the literature about possible uses of the traditional moment ratio diagram introduced by Karl Pearson, which uses the coefficient of skewness and of kurtosis to compare the shapes of various distributions commonly used in hydrology; (2) to complete this traditional MRD by integrating into it the regions occupied by the log-Pearson Type III and generalized gamma distributions which are more and more used in hydrology; (3) to present another MRD which uses ratios of moments of orders –1 (harmonic mean), quasi zero (geometric mean) and 1 (arithmetic mean); (4) to stress the need to consider the different MRD's (along with the more recently introduced L-moment ratio diagrams) as complementary tools for choosing between distributions fitted to hydrologic data. Finally, using Monte Carlo simulation we compare the two types of diagrams as tools to identify and discriminate between different distributions.