説明
<jats:p>It is well known that product moment ratio estimators of the coefficient of variation<jats:italic>C</jats:italic><jats:sub>ν</jats:sub>, skewness γ, and kurtosis κ exhibit substantial bias and variance for the small (<jats:italic>n</jats:italic>≤ 100) samples normally encountered in hydrologic applications. Consequently,<jats:italic>L</jats:italic>moment ratio estimators, termed<jats:italic>L</jats:italic>coefficient of variation τ<jats:sub>2</jats:sub>,<jats:italic>L</jats:italic>skewness τ<jats:sub>3</jats:sub>, and<jats:italic>L</jats:italic>kurtosis τ<jats:sub>4</jats:sub>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<jats:italic>C</jats:italic><jats:sub>ν</jats:sub>and γ are also remarkably biased for extremely large samples (<jats:italic>n</jats:italic>≥ 1000) from highly skewed distributions. A case study using large samples (<jats:italic>n</jats:italic>≥ 5000) of average daily streamflow in Massachusetts reveals that conventional moment diagrams based on estimates of product moments<jats:italic>C</jats:italic><jats:sub>ν</jats:sub>, γ, and κ reveal almost no information about the distributional properties of daily streamflow, whereas<jats:italic>L</jats:italic>moment diagrams based on estimators of τ<jats:sub>2</jats:sub>, τ<jats:sub>3</jats:sub>, and τ<jats:sub>4</jats:sub>enabled us to discriminate among alternate distributional hypotheses.</jats:p>
収録刊行物
-
- Water Resources Research
-
Water Resources Research 29 (6), 1745-1752, 1993-06
American Geophysical Union (AGU)