Examination of the Spencer-McCuen Outlier-Detection Test for Log-Pearson Type 3 Distributed Data
Publication: Journal of Hydrologic Engineering
Volume 21, Issue 3
Abstract
Identification of outliers in flood records can be an important step in a robust flood frequency analysis procedure. Bulletin 17B includes the Grubbs-Beck test (with ) as an objective criterion of whether the smallest observations in a flood record are outliers. The Spencer-McCuen test extends the Grubbs-Beck test to consider explicitly whether the three smallest observations are outliers in log-Pearson Type 3 (or equivalently Pearson Type 3) distributed samples with log-space skew coefficients between , and three significance levels [1, 5, and 10%]. Presented here are Monte Carlo experiments evaluating the performance of the Spencer-McCuen test. When that test relies on the sample skew coefficient as an estimate of the population skew, the test generally fails to achieve the nominal significance levels. The same is true when used with a generalized (weighted) skew coefficient. Thus, the test will often be inappropriate if used as originally proposed. More fundamentally, when a proposed test relies on the skew coefficient of a sample to test for outliers in that sample, it is no longer clear what it means for an observation to be an outlier.
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Acknowledgments
The authors would like to thank Rick McCuen and Tim Cohn for their constructive and very helpful comments. The authors would also like to thank Calvin Whealton, Xin Yu, and Jared Smith for reviewing early drafts of the manuscript.
References
Barnett, V., and Lewis, T. (1994). Outliers in statistical data, Wiley, New York.
Beckman, R. J., and Cook, R. D. (1983). “Outlier……….s.” Technometrics, 25(2), 119–149.
Cohn, T. A., England, J. F., Berenbrock, C. E., Mason, R. R., Stedinger, J. R., and Lamontagne, J. R. (2013). “A generalized Grubbs-Beck test for detecting multiple potentially influential low outliers in flood series.” Water Resour. Res., 49(8), 5047–5058.
Eash, D. A., Barnes, K. K., and Veilleux, A. G. (2013). “Methods for estimating annual exceedance-probability discharges for streams in Iowa, based on data through water year 2010.”, U.S. Geological Survey, Reston, VA, 63.
England, J. F., and Cohn, T. A. (2008). “Bulletin 17B flood frequency revisions: Practical software and test comparison results.” World Environmental and Water Resources Conf., K. C. Kabbes, ed., ASCE, Reston, VA.
England, J. F., Cohn, T. A., Faber, B. A., Stedinger, J. R., Thomas, W. O., and Mason, R. R. (2013). “Revisions Recommended to Bulletin 17B– US National Flood Frequency Guidelines.” American Geophysical Union Fall 2013 Meeting, American Geophysical Union, Washington, DC.
Feaster, T. D., Gotvald, A. J., and Weaver, J. C. (2009). “Magnitude and frequency of rural floods in the southeastern United States, 2006—Volume 3, South Carolina.”, USGS, Reston, VA, 226.
Gotvald, A. J., Feaster, T. D., and Weaver, J. C. (2009). “Magnitude and frequency of rural floods in the southeastern United States, 2006—Volume 1, Georgia.”, U.S. Geological Survey, Reston, VA, 120.
Griffis, V. W., and Stedinger, J. R. (2007). “The log-Pearson type 3 distribution and its application in flood frequency analysis. I: Distribution characteristics.” J. Hydrol. Eng., 482–491.
Grubbs, F. E. (1969). “Procedures for detecting outlying observations in samples.” Technometrics, 11, (1), 1–21.
Grubbs, F. E., and Beck, G. (1972). “Extension of sample sizes and percentage points for significance tests of outlying observations.” Technometrics, 14(4), 847–854.
IACWD (Interagency Advisory Committee on Water Data). (1982). “Guidelines for determining flood flow frequency (Bull. 17B).” U.S. Geological Survey, Reston, VA.
Lamontagne, J. R., Stedinger, J. R., Berenbrock, C., Veilleux, A. G., Ferris, J. C., and Knifong, D. L. (2012). “Development of regional skews for selected flood durations for the Central Valley Region, California, based on data through water year 2008.”, U.S. Geological Survey, Reston, VA, 60.
Lamontagne, J. R., Stedinger, J. R., Cohn, T. A., and Barth, N. A. (2013). “Robust national flood frequency guidelines: What is an outlier?” Proc., World Environmental and Water Resources Congress 2013, ASCE, Reston, VA.
Loucks, D. P., Stedinger, J. R., and Haith, D. A. (1983). Water resource systems planning and analysis, Prentice-Hall, Englewood Cliffs, NJ.
Parrett, C., Veilleux, A., Stedinger, J. R., Barth, N. A., Knifong, D. L., and Ferris, J. C. (2011). “Regional skew for California, and flood frequency for selected sites in the Sacramento-San Joaquin river basin, based on data through water year 2006.”, USGS, Reston, VA, 94.
Spencer, C. S., and McCuen, R. H. (1996). “Detection of outliers in Pearson type III data.” J. Hydrol. Eng., 2–10.
Stedinger, J. R., and Griffis, V. W. (2008). “Flood frequency analysis in the United States: Time to update.” J. Hydrol. Eng., 199–204.
Thomas, W. (1985). “A uniform technique for flood frequency analysis.” J. Water Resour. Plann. Manage., 321–337.
Vogel, R. W., and McMartin, D. E. (1991). “Probability plot goodness-of-fit and skewness estimation procedures for the Pearson type 3 distribution.” Water Resour. Res., 27(12), 3149–3158.
Weaver, J. C., Feaster, T. D., and Gotvald, A. J. (2009). “Magnitude and frequency of rural floods in the southeastern United States, 2006—Volume 2, North Carolina.” Rep. 2009–5158, USGS, Reston, VA, 113.
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Journal of Hydrologic Engineering
Volume 21 • Issue 3 • March 2016
Copyright
© 2015 American Society of Civil Engineers.
History
Received: Mar 26, 2015
Accepted: Sep 23, 2015
Published online: Nov 19, 2015
Published in print: Mar 1, 2016
Discussion open until: Apr 19, 2016
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