L-moment ratio diagrams are increasingly being used in the literature for s
electing a probability distribution function for regional frequency analysi
s. Two graphical methods are often used in the distribution selection proce
ss, the sample average and a line of best-fit through the sample L-moment r
atios. Examples of homogeneous and heterogeneous regional samples are simul
ated to illustrate the utility of the two distribution selection methods. D
istribution selection for homogeneous regional data is best based on the sa
mple average and not on a line of best-fit through the data points. For ver
y heterogeneous regional data, exhibiting a large range in the distribution
s shape parameter, the line of best-fit is useful for distribution selectio
n. These results emphasize the importance of using heterogeneity tests in c
onjunction with L-moment ratio diagrams.