Lmoment diagrams should replace product moment diagrams

摘要

It is well known that product moment ratio estimators of the coefficient of variationCν, skewness γ, and kurtosis κ exhibit substantial bias and variance for the small (n≤ 100) samples normally encountered in hydrologic applications. Consequently,Lmoment ratio estimators, termedLcoefficient of variation τ2,Lskewness τ3, andLkurtosis τ4are 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 ofCνand 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 momentsCν, γ, and κ reveal almost no information about the distributional properties of daily streamflow, whereasLmoment diagrams based on estimators of τ2, τ3, and τ4enabled us to discriminate among alternate distri