L-MOMENT DIAGRAMS SHOULD REPLACE PRODUCT MOMENT DIAGRAMS

It is well known that product moment ratio estimators of the coefficient of variation C(upsilon) skewness gamma, and kurtosis kappa exhibit substantial bias and variance for the small (n less-than-or-equal-to 100) samples normally encountered in hydrologic applications. Consequently, 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 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 C(upsilon) and gamma are also remarkably biased for extremely large samples (n greater-than-or-equal-to 1000) from highly skewed distributions. A case study using large samples (n greater-than-or-equal-to 5000) of average daily streamflow in Massachusetts reveals that conventional moment diagrams based on estimates of product moments C(upsilon), gamma, and kappa reveal almost no information about the distributional properties of daily streamflow, whereas L moment diagrams based on estimators of tau2, tau3, and tau4 enabled us to discriminate among alternate distributional hypotheses.