TECHNICAL PAPERS
Jan 1, 1998

Effect of Trimming on LP III Flood Quantile Estimates

Publication: Journal of Hydrologic Engineering
Volume 3, Issue 1

Abstract

In the fields of statistics and hydrology, a considerable amount of research has been directed toward robust methods of estimation. This paper broadly reviews these methods and presents results of the application of a specific robust estimation procedure, namely trimming, in flood frequency analysis. Using simulation, the effect of various proportions of symmetric trimming on the estimation of moments, distribution parameters, and quantiles is examined. The influence of the sample size and parent distribution parameters on the estimation performance is also investigated for several return periods and for three different fitting methods for the log-Pearson Type III distribution. While the results point to the potential usefulness of robust estimators in hydrological analysis, they also serve as a precaution that certain distribution fitting techniques may be overly robust to extreme observations in the sample (those in the tails).

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References

1.
Andrews, D. F., Bickel, P. J., Hampel, F. R., Huber, P. J., Rogers, W. H., and Tukey, J. W. (1972). Robust estimates of location: survey and advances. Princeton University Press, Princeton, N.J.
2.
Ashkar, F., and Ouarda, T. B. M. J. (1996). “On some methods of fitting the generalized Pareto distribution.”J. of Hydro., Amsterdam, The Netherlands, 177(1–2), 117–141.
3.
Benson, M. A.(1968). “Uniform flood frequency estimation methods for federal agencies.”Water Resour. Res., 4(5), 891–908.
4.
Bickel, P. J.(1965). “On some robust estimates of location.”Ann. Math. Statistics, 36, 847–858.
5.
Bobée, B.(1975). “The log-Pearson type III distribution and its application in hydrology.”Water Resour. Res., 11(5), 681–689.
6.
Bobée, B., and Ashkar, F. (1988). “Sundry averages method for estimating parameters of the log-Pearson type III distribution.”Rapport Scientifique No. 251, INRS-Eau, Sainte-Foy, Canada.
7.
Bobée, B., and Ashkar, F. (1991). The gamma family and derived distributions applied in hydrology. Water Resources Publications, Littleton, Colo.
8.
Box, G. E. P.(1977). “Discussion of `Do robust estimators work with real data?”' by S. M. Stigler, Ann. of Statistics, 5(6), 1081–1083.
9.
Boyer, J. E., and Kolson, J. O.(1983). “Variances for adaptive trimmed means.”Biometrika, 70(1), 97–102.
10.
Crow, E. L., and Siddiqui, M. M.(1967). “Robust estimates of location.”J. Am. Statistical Assn., 62(1), 353–389.
11.
David, F. N., and Johnson, N. L.(1954). “Statistical treatment of censored data, I. Fundamental formulae.”Biometrika, 41(1), 228–240.
12.
Efron, B., and Morris, C.(1977). “Stein's paradox in statistics.”Scientific American, 236(5), 119–127.
13.
Fiering, M. B., Harrington, J., and Rogers, P. P. (1978). “Standards, optimality and resilience in water-resource management.”Rep. Prepared for U.S. Dept. of the Interior, OWRT, Contract 14-34-0001-6208, Cambridge, Mass.
14.
Harter, H. L., and Moore, A. H.(1966). “Iterative maximum likelihood estimation of the parameters of normal populations from singly and doubly censored samples.”Biometrika, 53(2), 205–213.
15.
Hogg, R. V.(1974). “Adaptive robust procedures: a partial review and some suggestions for future applications and theory.”J. Am. Statistical Assn., 69(348), 909–923.
16.
Houghton, J. (1977). “Robust estimation of the frequency of extreme events in a flood frequency context,” Doctoral dissertation, Harvard Univ., Cambridge, Mass.
17.
Huber, P. J.(1972). “Robust statistics: a review.”Ann. Math. Statistics, 43(4), 1041–1067.
18.
Institution of Engineers of Australia (IEA). (1977). “Australian rainfall and runoff: flood analysis and design.”Rep., IEA, Canberra, Australia.
19.
Joiner, B. L., and Rosenblatt, J. R.(1971). “Some properties of the range in samples from Tukey's symmetric lambda distributions.”J. Am. Statistical Assn., 66, 394–399.
20.
Kroll, C. N., and Stedinger, J. R.(1996). “Estimation of moments and quantiles using censored data.”Water Resour. Res., 32(4), 1005–1012.
21.
Kuczera, G.(1982). “Robust flood frequency models.”Water Resour. Res., 18(2), 315–324.
22.
Landwehr, J. M., Matalas, N. C., and Wallis, J. R.(1978). “Some comparisons of flood statistics in real and log space.”Water Resour. Res., 14(5), 902–920.
23.
Moran, P. A. P.(1957). “The statistical treatment of flood flows.”EOS Trans. AGU., 58(4), 519–523.
24.
Nozdryn-Plotnicki, M. J., and Watt, W. E.(1979). “Assessment of fitting techniques for the log Pearson type III distribution using Monte Carlo simulation.”Water Resour. Res., 15(3), 714–718.
25.
Phatarfod, R. N.(1977). “The sampling error of storage size.”Water Resour. Res., 13(6), 967–969.
26.
Phien, H. N., and Fang, T.-S. E. (1989). “Maximum likelihood estimation of the parameters and quantiles of the general extreme-value distribution from censored samples.”J. Hydro., Amsterdam, The Netherlands, 105(1,2), 139–155.
27.
Prescott, P.(1978). “Selection of trimming proportions for robust adaptive trimmed means.”J. Am. Statistical Assn., 73(361), 133–140.
28.
Rao, D. V.(1980). “Log-Pearson type III distribution, method of mixed moments.”J. Hydr. Div., ASCE, 106(6), 999–1019.
29.
Rao, D. V.(1983). “Estimating log-Pearson parameters by mixed moments.”J. Hydr. Div. Engrg., 109(8), 1119–1132.
30.
Rocke, D. M., and Downs, G. W. (1981). “Estimating the variances of robust estimators of location: influence curve, jacknife and bootstrap.”Communications in Statistics—Simulation and Computation, B10(3), 221–248.
31.
Rocke, D. M., Downs, G. W., and Rocke, A. J.(1982). “Are robust estimators really necessary?”Technometrics, 24(2), 95–101.
32.
Siddiqui, M. M., and Raghunandanan, K.(1967). “Asymptotically robust estimators of location.”J. Am. Statistical Assn., 62(1), 950–953.
33.
Smith, J. A.(1987). “Estimating the upper tail of flood frequency distributions.”Water Resour. Res., 23(8), 1657–1666.
34.
Stigler, S. M.(1973). “The asymptotic distribution of the trimmed mean.”Ann. of Statistics, 1(3), 472–477.
35.
Stigler, S. M.(1977). “Do robust estimators work with real data?”Ann. of Statistics, 5(6), 1055–1098.
36.
Tiku, M. L.(1967). “Estimating the mean and standard deviation from censored normal samples.”Biometrika, 54(1), 155–165.
37.
Tiku, M. L.(1980). “Robustness of MML estimators based on censored samples and robust test statistics.”J. Statistical Plng. and Inference, 4(2), 123–143.
38.
Tiku, M. L.(1982). “Robust statistics for testing equality of means or variances.”Commun. Statistics—Theoretical Methods, 11(22), 2543–2558.
39.
Tukey, J. W., and McLaughlin, D. H. (1963). “Less vulnerable confidence and significance procedures for location based on a single sample (trimming Winsorization I).”Sankhya, Ser. A 25, 331–352.
40.
Wang, Q. J. (1990). “Estimation of the GEV distribution from censored samples by method of partial probability weighted moments.”J. Hydro., 120(1–4), 103–114.
41.
Water Resources Council (WRC). (1977). “Guidelines for determining flood-flow frequency.”Bull. 17A, Hydro., Committee, Washington, D.C.

Information & Authors

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Go to Journal of Hydrologic Engineering
Journal of Hydrologic Engineering
Volume 3Issue 1January 1998
Pages: 33 - 42

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Published online: Jan 1, 1998
Published in print: Jan 1998

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Authors

Affiliations

Taha B. M. J. Ouarda
Res. Assoc., INRS-Eau, 2800 Einstein, C.P. 7500, Ste-Foy, PQ, G1V 4C7, Canada.
Fahim Ashkar
Prof., Dept. of Math. and Statistics, Univ. of Moncton, Moncton, NB, E1A 3E9, Canada.

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