Confidence Interval for Design Floods with Estimated Skew Coefficient
Publication: Journal of Hydraulic Engineering
Volume 117, Issue 7
Abstract
In 1983, Stedinger published a method, based on the noncentral t‐ distribution, for constructing approximate confidence intervals for quantiles of a Pearson type‐3 (P3) distribution when the coefficient of skewness is known. That method is extended to the case when the coefficient of skewness is estimated by either (1) The at‐site sample skew; (2) a generalized regional‐average skew; or (3) a weighted average skew. The confidence intervals perform satisfactorily in Monte Carlo simulations. Confidence intervals generated using a three‐parameter asymptotic method and the Water Resources Council method, which ignores uncertainty in the weighted skew, perform poorly. The actual confidence of confidence intervals for a design flood can be much lower than the target if uncertainty in the skewness coefficient is ignored. It is important to distinguish between the sampling variability in the sample skew coefficient at the site and the likely variation of the true skews in the region when estimating the precision of a generalized skewness coefficient for the region. Five approximations of frequency factors for the P3 distribution are also evaluated.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Arnell, N. W. (1989). “Expected annual damages and uncertainties in flood frequency estimation,” J. Water Resour. Planning Mgmt., ASCE, 115(1), 94–107.
2.
Arora, K., and Singh, V. P. (1989). “A comparative evaluation of the estimators of the log Pearson type (LP) 3 distribution.” J. Hydrol., 105(1/2), 19–37.
3.
Bao, Y., Tung, Y. K., and Hasfurther, V. R. (1987). “Evaluation of uncertainties in flood magnitude estimator on annual expected damage cost of hydraulic structures.” Water Resour. Res., 23(11), 2023–2029.
4.
Bobee, B. (1973). “Sample error of T‐year events computed by fitting a Pearson type 3 distribution.” Water Resour. Res., 9(5), 1264–1270.
5.
Bobee, B. (1975). “The log Pearson type 3 distribution and its application in hydrology.” Water Resour. Res., 11(5), 681–689.
6.
Bobee, B. (1979). Discussion of “Fitting the Pearson type 3 distribution in practice.” by J. Buckett and F. R. Oliver. Water Resour. Res., 15(3), 730.
7.
Bobee, B., and Robitaille, R. (1975). “Correction of bias in the estimation of the coefficient of skewness.” Water Resour. Res., 11(6), 851–854.
8.
Bobee, B., and Robitaille, R. (1977). “The use of the Pearson type 3 and log‐Pearson type 3 distributions revisited.” Water Resour. Res., 13(2), 427–443.
9.
Chow, V. T. (1964). Handbook of applied hydrology. Ch. 8, McGraw‐Hill, New York, N.Y.
10.
“Guidelines for determining flood flow frequency.” (1977). Bulletin #17A, Appendix 9, Water Resour. Council, Hydrology Committee, Washington, D.C.
11.
“Guidelines for determining flood flow frequency.” (1981). Bulletin #17B, Appendix 9, Water Resour. Council, Hydrology Committee, Washington, D.C.
12.
“Guidelines for determining flood flow frequency.” (1982). Bulletin #17B, Interagency Advisory Committee on Water Data, U.S. Geological Survey, Reston, Va.
13.
Hardison, C. H. (1974). “Generalized skew coefficients of annual floods in the United States and their application.” Water Resour. Res., 10(4), 745–752.
14.
Harter, H. L. (1969). “A new table of percentage points of the Pearson type III distribution.” Technometrics, 11(1), 177–187.
15.
Hoshi, K., and Burges, S. J. (1981a). “Sampling properties of parameter estimates for the log Pearson type 3 distribution, using moments in real space.” J. Hydrol., 53(3/4), 305–316.
16.
Hoshi, K., and Burges, S. J. (1981b). “Approximate estimation of the derivative of a standard gamma quantile for use in confidence interval estimates.” J. Hydro., 53(3/4), 317–325.
17.
Hu, S. (1987). “Determination of confidence intervals for design floods.” J. Hydro., 96(1–4), 201–213.
18.
James, L. D., and Hall, B. (1986). “Risk information for floodplain management.” J. Water Resour. Planning Mgmt., ASCE, 112(4), 485–499.
19.
Kirby, W. (1972). “Computer‐oriented Wilson‐Hilferty transformation that preserves the first three moments and the lower bound of the Pearson type 3 distribution.” Water Resour. Res., 8(5), 1251–1254.
20.
Kite, G. W. (1975). “Confidence limits for design events.” Water Resour. Res., 11(1), 48–53.
21.
Kite, G. W. (1976). Reply to comment on “Confidence limits for design events.” Water Resour. Res., 12(4), 826.
22.
Kite, G. W. (1988). Frequency and Risk Analysis in Hydrology. Ch. 9, 10, and 15, Water Resources Publications, Colorado (revised).
23.
Lall, U., and Beard, L. R. (1982). “Estimation of Pearson type 3 moments.” Water Resour. Res., 18(5), 1563–1569.
24.
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.
25.
Lettenmaier, D. P., and Burges, S. J. (1980). “Correction for bias in estimation of the standard deviation and coefficient of skewness of the log Pearson 3 distribution.” Water Resour. Res., 16(4), 762–766.
26.
Loucks, D. P., Stedinger, J. R., and Haith, D. A. (1981). Water resources systems planning and analysis. Ch. 3, Prentice‐Hall, Inc., Englewood Cliffs, N.J.
27.
McCuen, R. H. (1979). “Map skew???.” J. Water Resour. Planning Mgmt., ASCE, 105(2), 269–277.
28.
McGinnis, D. G., and Sammons, W. H. (1970). Discussion of “Daily stream flow simulation,” by K. Payne, W. R. Neuman, and K. P. Kerri, J. Hydr. Div., ASCE, 96(5), 1201–1206.
29.
McMahon, T. A., and Miller, A. J. (1967). “Application of the Thomas and Fiering model to skewed hydrologic data.” Water Resour. Res., 3(4), 937–946.
30.
Nozdryn‐Plotnicki, M. J., and Watt, W. E. (1979). “Assessment of fitting techniques for the log Pearson type 3 distribution using Monte Carlo simulation.” Water Resour. Res., 15(3), 714–718.
31.
Phien, H. N., and Hsu, L. C. (1985). “Variance of the T‐year event in the log‐Pearson type‐3 distribution.” J. Hydrol., 77(1/4), 141–158.
32.
Stedinger, J. R. (1980). “Fitting log normal distributions to hydrologic data.” Water Resour. Res., 16(3), 481–490.
33.
Stedinger, J. R. (1983a). “Confidence intervals for design events.” J. Hydr. Engrg., ASCE, 109(1), 13–27.
34.
Stedinger, J. R. (1983b). “Design events with specified flood risk.” Water Resour. Res., 19(2), 511–522.
35.
Tasker, G. D. (1978). “Flood frequency analysis with a generalized skew coefficient.” Water Resour. Res., 14(2), 373–376.
36.
Tasker, G. D., and Stedinger, J. R. (1986). “Regional skew with weighted LS regression.” J. Water Resour. Planning Mgmt., ASCE, 112(2), 225–237.
37.
Tung, Y. K. (1987). “Effects of uncertainties on optimal risk‐based design of hydraulic structures.” J. Water Resour. Planning Mgmt., ASCE, 113(5), 709–722.
38.
Tung, Y. K., and Mays, L. W. (1981). “Reducing hydrologic parameter uncertainty,” J. Water Resour. Planning Mgmt., ASCE, 107(1), 245–262.
39.
Wallis, J. R., Matalas, N. C., and Slack, J. R. (1974). “Just a moment!.” Water Resour. Res., 10(2), 211–219.
40.
Whitley, R. J., and Hromadka, T. V. (1987). “Estimating 100‐year flood confidence intervals.” Adv. Water Resour., 10, 225–227.
41.
Wilson, E. B., and Hilferty, M. M. (1931). “The distribution of Chi‐square.” Proc. National Academy Sci., 17, 684–688.
42.
Zelen, M., and Severo, N. C. (1964). “Probability functions.” Handbook of Mathematical Functions, M. Abramowitz and I. A. Stegun, eds., Ch. 26, U.S. National Bureau of Standards, Washington, D.C.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 117 • Issue 7 • July 1991
Pages: 811 - 831
Copyright
Copyright © 1991 ASCE.
History
Published online: Jul 1, 1991
Published in print: Jul 1991
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.