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

[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.

[1]  Jery R. Stedinger,et al.  Plotting positions for historical floods and their precision , 1987 .

[2]  Jery R. Stedinger,et al.  Estimation of Moments and Quantiles using Censored Data , 1996 .

[3]  M. Bartlett,et al.  APPROXIMATE CONFIDENCE INTERVALS , 1953 .

[4]  Richard H. McCuen,et al.  Generalized Flood Skew: Map versus Watershed Skew , 2001 .

[5]  Renzo Rosso,et al.  Statistics, Probability and Reliability for Civil and Environmental Engineers , 1997 .

[6]  Jose D. Salas,et al.  Data-based comparisons of moments estimators using historical and paleoflood data , 2003 .

[7]  W. L. Lane,et al.  Confidence intervals for expected moments algorithm flood quantile estimates , 2001 .

[8]  T. V. Hromadka,et al.  Approximate confidence intervals for design floods for a single site using a neural network , 1999 .

[9]  Jose D. Salas,et al.  Comparisons of two moments‐based estimators that utilize historical and paleoflood data for the log Pearson type III distribution , 2003 .

[10]  Wilbert O. Thomas,et al.  A Uniform Technique for Flood Frequency Analysis , 1985 .

[11]  Jery R. Stedinger,et al.  Confidence Interval for Design Floods with Estimated Skew Coefficient , 1991 .

[12]  W. L. Lane,et al.  An algorithm for computing moments‐based flood quantile estimates when historical flood information is available , 1997 .

[13]  Jery R. Stedinger,et al.  Regional Skew with Weighted LS Regression , 1986 .

[14]  Richard H. McCuen,et al.  DETECTION OF OUTLIERS IN PEARSON TYPE III DATA , 1996 .

[15]  H. A. David,et al.  Order Statistics (2nd ed). , 1981 .

[16]  M. E. Jennings,et al.  Frequency Curves for Annual Flood Series with Some Zero Events or Incomplete Data , 1969 .

[17]  C. H. Hardison,et al.  Generalized skew coefficients of annual floods in the United States and their application , 1974 .

[18]  Edward M. Tomlinson,et al.  Regional interdisciplinary paleoflood approach to assess extreme flood potential , 2000 .

[19]  J. R. Wallis,et al.  Just a Moment , 2013 .

[20]  Timothy A. Cohn,et al.  Estimation of descriptive statistics for multiply censored water quality data , 1988 .

[21]  Robert J. Gilliom,et al.  Estimation of Distributional Parameters for Censored Trace Level Water Quality Data: 1. Estimation Techniques , 1986 .

[22]  Toby D. Feaster,et al.  TECHNIQUES FOR ESTIMATING THE MAGNITUDE AND FREQUENCY OF FLOODS IN RURAL BASINS OF SOUTH CAROLINA, 1999 , 2002 .

[23]  B. Bobée.  Sample error of T‐year events commuted by fitting a Pearson type 3 distribution , 1973 .

[24]  Gary D. Tasker,et al.  Flood frequency analysis with a generalized skew coefficient , 1978 .

[25]  N. C. Matalas,et al.  Some comparisons of flood statistics in real and log space , 1978 .

[26]  Jery R. Stedinger,et al.  Bayesian GLS Regression with Application to LP3 Regional Skew Estimation , 2003 .

[27]  J. Stedinger.  Frequency analysis of extreme events , 1993 .