Regional Hydrologic Analysis, 2, Model‐Error Estimators, Estimation of Sigma and Log‐Pearson Type 3 Distributions

Abstract

For a number of cases, weighted and generalized least squares regression procedures were shown by Stedinger and Tasker (1985, 1986) to provide better estimators of the parameters of models of hydrologic statistics as a function of drainage basin characteristics. These procedures require estimation of the true model's standard error of prediction. Evaluated here are three model error estimators for weighted least squares (WLS) regression and two for generalized least squares (GLS) regression. The generalized mean square estimator employed by Stedinger and Tasker (1985) was nearly unbiased, and comparable in accuracy to and easier to compute than the maximum likelihood estimator. GLS and WLS regression estimators of the log‐streamflows' standard deviation are shown to be substantially more accurate than ordinary least squares estimators. Finally, the consequences and impact of nonlognormal streamflows were evaluated. In the cases considered, GLS procedures continued to perform well even when the normality assumption was violated.