EMA with Historical Information, Low Outliers, and Regional Skew

Abstract

The Federal guidelines for flood frequency analysis described by Bulletin 17B employ three separate procedures to reflect historical flood information, to account for censored low outliers, and to introduce regional skew. Further, the identification of outliers and the moments of the final fitted log-Pearson type 3 (LP3) distribution are dependent on the order in which these procedures are employed. Alternatively, the recently developed expected moments algorithm (EMA) for the LP3 distribution combines these three steps into one consistent analysis. Previous studies have demonstrated that EMA does as well as maximum likelihood estimators at estimating LP3 flood quantiles using historical information. EMA is also more efficient than the Bulletin 17B historically weighted moments algorithm, and can incorporate a wider range of historical information, including thresholds that were never exceeded, and floods whose values are described by intervals. Modest differences have been observed in the performance of EMA for low outlier adjustments relative to the Bulletin 17B conditional probability adjustment. Still, an analysis is needed of the performance of the EMA procedure which simultaneously employs historical information, regional skew information, and adjustments for any low outliers. A Monte Carlo analysis clearly demonstrates that this EMA estimator is more efficient than the Bulletin 17B estimator employing the same information.