Are L-moment Ratio Diagrams Useful for Distribution Selection for Frequency Analysis?

L-moment ratio diagrams are increasingly being used in the literature for selecting a probability distribution function for frequency analysis. Generally two methods are used in the distribution selection process, the sample average and, more recently, a line of best fit through the sample L-moment ratios which is then compared to the theoretical curve of each candidate distribution. Monte Carlo simulations of homogeneous and heterogeneous samples were used to investigate these two selection methods. The sample average performed well in all homogeneous scenarios and poorly in all heterogeneous scenarios. The line of best fit performed poorly in all homogeneous scenarios and with mixed results in the heterogeneous scenarios. Distribution selection, using L-moment ratio diagrams, for homogeneous data is best based on the sample average and not on a line of best fit through the data points. For heterogeneous data, L-moment ratio diagrams are in theory useful for distribution selection only when data are drawn from a single distribution function with evenly mixed parent values of the shape parameter. Under this condition, the line of best fit tends to follow the theoretical curve of the parent distribution function. In practice, however, there are no means of knowing whether real data are drawn as such.