It is well known that product moment ratio estimators of the coefficient of variation Cv, skewness &ggr;, and kurtosis &kgr; exhibit substantial bias and variance for the small (n≤100) samples normally encountered in hydrologic applications. Consequently, L moment ratio estimators, termed L coefficient of variation &tgr;2, L skewness &tgr;3, and L kurtosis &tgr;4 are now advocated because they are nearly unbiased for all underlying distributions. The advantages of L moment ratio estimators over product moment ratio estimators are not limited to small samples. Monte Carlo experiments reveal that product moment estimators of Cv and &ggr; are also remarkably biased for extremely large samples (n≥1000) from highly skewed distributions. A case study using large samples (n≥5000) of average daily streamflow in Massachusetts reveals that conventional moment diagrams based on estimates of product moments Cv, &ggr;, and &kgr; reveal almost no information about the distributional properties of daily streamflow, whereas L moment diagrams based on estimators of &tgr;2, &tgr;3, and &tgr;4 enabled us to discriminate among alternate distributional hypotheses. ¿ American Geophysical Union 1993