Log Pearson type 3 quantile estimators with regional skew information and low outlier adjustments

Abstract

[1] The recently developed expected moments algorithm (EMA) [Cohn et al., 1997] does as well as maximum likelihood estimations at estimating log-Pearson type 3 (LP3) flood quantiles using systematic and historical flood information. Needed extensions include use of a regional skewness estimator and its precision to be consistent with Bulletin 17B. Another issue addressed by Bulletin 17B is the treatment of low outliers. A Monte Carlo study compares the performance of Bulletin 17B using the entire sample with and without regional skew with estimators that use regional skew and censor low outliers, including an extended EMA estimator, the conditional probability adjustment (CPA) from Bulletin 17B, and an estimator that uses probability plot regression (PPR) to compute substitute values for low outliers. Estimators that neglect regional skew information do much worse than estimators that use an informative regional skewness estimator. For LP3 data the low outlier rejection procedure generally results in no loss of overall accuracy, and the differences between the MSEs of the estimators that used an informative regional skew are generally modest in the skewness range of real interest. Samples contaminated to model actual flood data demonstrate that estimators which give special treatment to low outliers significantly outperform estimators that make no such adjustment.

Bayesian MCMC flood frequency analysis with historical information

“…EMA was extended to include regional skew information in Griffis et al (2004). Kuczera (1996) discusses problems posed by measurement errors and uses a maximum likelihood procedure to incorporate the distribution of possible measurement errors into an analysis for the threeparameter GEV distribution.…”

A generalized Grubbs‐Beck test statistic for detecting multiple potentially influential low outliers in flood series

“…First, efficient censored-data estimators are more challenging conceptually and numerically than the relatively straightforward closed-form estimators that employ complete data sets [Griffis et al, 2004]. The availability of good statistical software solves that problem.…”

“…It can be used to construct a one-sided variation of the Rosner [1983] test. Once such low outliers have been identified, they can be treated as ''less-than'' values, thereby increasing robustness of the frequency analysis without substantially reducing the precision with which moments-based fitting methods such as EMA [Cohn et al, 1997;Griffis et al, 2004] can estimate the flood quantiles of interest. or conversely…”

“…The present work is motivated by ongoing efforts [England and Cohn, 2008;Stedinger and Griffis, 2008] to explore potential improvements to Bulletin 17B [IACWD, 1982] with moments-based, censored-data alternatives [Cohn et al, 1997;Griffis et al, 2004]. The proposed statistic is constructed following the reasoning in Rosner [1975], who developed a two-sided R-Statistic ''many outlier'' test (RST), that is based on the following argument:…”

Application of New Version of Flood Frequency Analysis (Bulletin 17C)

“…Expected Moment Algorithms (EMA)은 Pearson Type-III (P-III) 분포형의 매개변수를 산정하기 위한 모멘트법을 일반화한 것이라 할 수 있다 (Cohn et al, 2013;England Jr, 2004;England Jr and Cohn, 2008;England Jr et al, 2003;Griffis et al, 2004). 특히 중도절단자료(censored data)를 매개변수 추정에 활용할 수 있도록 해주는데, 이는 Bulletin 17C의 주요 핵심 중 하나이다 (Cohn et al, 1997).…”