L moment diagrams should replace product moment diagrams

It is well known that product moment ratio estimators of the coefficient of variation C ν , skewness γ, and kurtosis κ 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 τ 2 , L skewness τ 3 , and L kurtosis τ 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 C ν and γ 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 C ν , γ, and κ reveal almost no information about the distributional properties of daily streamflow, whereas L moment diagrams based on estimators of τ 2 , τ 3 , and τ 4 enabled us to discriminate among alternate distributional hypotheses.