SMEMAX? Caution!
Publication: Journal of Hydraulic Engineering
Volume 110, Issue 3
Abstract
The SMEMAX Transformation was tested on samples generated from log‐Pearson Type III and Gumbel Extreme Value Type 1 distributions. Although the transformation results in a distribution with a skew near zero, it is not a true normal distribution. The coefficients of kurtosis for the transformed distributions are always less than three and when the parent distribution approaches a reverse‐J shape, the transformed distribution is bimodal. When the skew coefficient of the logarithms of events is or greater for samples from the log‐Pearson Type III distribution, the SMEMAX procedure underestimates the magnitude of events with return periods of 50 yr and greater. Similarly, SMEMAX estimates of rare events from the Gumbel Extreme Value Type 1 distribution are always too low. Based on comparisons made in this study, it is likely that application of SMEMAX procedures to any skewed distribution will result in biased estimates of the magnitude of rate events and if the skew is positive the estimates will be too low.
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References
1.
Bethlahmy, N., “Flood Analysis by SMEMAX Transformation,” Journal of the Hydraulics Division, ASCE, Vol. 103, No. HY1, Proc. Paper 12701, Jan., 1977, pp. 69–78.
2.
“Guidelines for Determining Flood Flow Frequency,” Bulletin No. 17A, United States Water Resources Council, Hydrology Committee, Washington, D.C., revised June, 1977.
3.
Jorgensen, L. N., et al., “California Streamflow Characteristics, Volume 1,” Open‐File Report, United States Department of the Interior, Geological Survey, Water Resources Division, Menlo Park, Calif., June 7, 1971.
4.
Jorgensen, L. N., et al., “California Streamflow Characteristics, Volume 2,” Open‐File Report, United States Department of the Interoir, Geological Survey, Water Resources Division, Menlo Park, Calif., June 7, 1971.
5.
Lettenmaier, D. P., and Burges, S. J., “Gumbel's Extreme Value I Distribution: A New Look,” Journal of the Hydraulics Division, ASCE, Vol. 108, No. HY4, Proc. Paper 17007, Apr., 1982, pp. 502–514.
6.
Rasheed, H. R., Ramamoorthy, M. V., and Al‐Dabbagh, A. S., “Modified SMEMAX Transformation for Frequency Analysis,” Water Resources Bulletin, American Water Resources Association, Vol. 1B, No. 3, June, 1982, pp. 509–512.
7.
Shahidi, M., and Walker, H. H., discussion of “Flood Analysis by SMEMAX Transformation,” by Nedavia Bethlahmy, Journal of the Hydraulics Division, ASCE, Vol. 104, No. HY3, Proc. Paper 12701, Mar., 1978, pp. 449–451.
Information & Authors
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Published In
Journal of Hydraulic Engineering
Volume 110 • Issue 3 • March 1984
Pages: 209 - 218
Copyright
Copyright © 1984 ASCE.
History
Published online: Mar 1, 1984
Published in print: Mar 1984
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