The log Pearson type 3 distribution and its application in flood frequency analysis. III

Abstract

The accuracy of flood quantile estimates is constrained by the data available at a site. To improve the accuracy of quantile estimators, Bulletin 17B recommends combining the station skew with a regional skew using the inverse of their mean square errors MSEs as weights. While these weights can yield the minimum MSE skewness estimator, they do not provide the minimum MSE quantile estimators except when the true at-site skew is zero. In this paper, optimal weights which provide minimum MSE quantile estimators are derived. A Monte Carlo experiment illustrates the value of different weighting schemes and the value of using an informative regional skew. For reasonable values of the regional skew, the MSE of quantile estimators is reduced when the sample skew is combined with an informative regional skew. Modest improvements in the MSE of quantile estimates are obtained using optimal quantile weights rather than the MSE-skew weights. When the regional skew is actually very informative, there is a large loss of efficiency for positively skewed populations when either weight is incorrectly computed using a regional skew estimation error of 0.302 as recommended by the map in Bulletin 17B. Approximations for the MSE, variance, and bias of sample skewness estimators are provided with accuracies on the order of 0.1%. In addition, a factor for unbiasing skewness estimators for 1.414 is developed for use in regional skew studies.