L-MOMENT DIAGRAMS SHOULD REPLACE PRODUCT MOMENT DIAGRAMS

It is well known that product moment ratio estimators of the coefficie nt of variation C(upsilon) skewness gamma, and kurtosis kappa exhibit substantial bias and variance for the small (n less-than-or-equal-to 1 00) samples normally encountered in hydrologic applications. Consequen tly, L moment ratio estimators, termed L coefficient of variation tau2 , L skewness tau3, and L kurtosis tau4 are now advocated because they are nearly unbiased for all underlying distributions. The advantages o f L moment ratio estimators over product moment ratio estimators are n ot limited to small samples. Monte Carlo experiments reveal that produ ct moment estimators of C(upsilon) and gamma are also remarkably biase d for extremely large samples (n greater-than-or-equal-to 1000) from h ighly skewed distributions. A case study using large samples (n greate r-than-or-equal-to 5000) of average daily streamflow in Massachusetts reveals that conventional moment diagrams based on estimates of produc t moments C(upsilon), gamma, and kappa reveal almost no information ab out the distributional properties of daily streamflow, whereas L momen t diagrams based on estimators of tau2, tau3, and tau4 enabled us to d iscriminate among alternate distributional hypotheses.