Confidence Interval for Design Floods with Estimated Skew Coefficient

Abstract

In 1983, Stedinger published a method, based on the noncentral t‐ distribution, for constructing approximate confidence intervals for quantiles of a Pearson type‐3 (P3) distribution when the coefficient of skewness is known. That method is extended to the case when the coefficient of skewness is estimated by either (1) The at‐site sample skew; (2) a generalized regional‐average skew; or (3) a weighted average skew. The confidence intervals perform satisfactorily in Monte Carlo simulations. Confidence intervals generated using a three‐parameter asymptotic method and the Water Resources Council method, which ignores uncertainty in the weighted skew, perform poorly. The actual confidence of confidence intervals for a design flood can be much lower than the target if uncertainty in the skewness coefficient is ignored. It is important to distinguish between the sampling variability in the sample skew coefficient at the site and the likely variation of the true skews in the region when estimating the precision of a generalized skewness coefficient for the region. Five approximations of frequency factors for the P3 distribution are also evaluated.