Abstract
A mixed method combining the method of moments and the method of optimization (MMO) was developed for estimating the parameters of the log-Pearson type 3 (LP3) distribution. The MMO estimates the parameters of mean and standard deviation by the method of indirect moments (MIM) and estimates the coefficient of skewness by minimizing both the relative root average square error (RRASE) and the relative average bias (RAB). Both the predictive capability and descriptive capability of six popular estimation methods were evaluated using 90 sets of observed flood data and six selected LP3 populations with 1000 samples for each selected sample size. The performance of the MMO was compared with those of five other selected estimation methods. A weighted ranking index (WRI) procedure was developed to help select the best combination of distribution and method for the Louisiana flood data. The WRI takes both the predictive capability and the descriptive capability into account in the evaluation. The combination of LP3/MMO was found to be the best combination for Louisiana flood data.
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References
Arora, K.; Singh, V.P. 1989: A comparative evaluation of the estimators of the logPearson type 3 distribution. J. Hydrology 105, 19–37, The Netherlands
Bobée, B. 1975: The log-Pearson type 3 distribution and its application hydrology. Water Resources Research 11(5), 681–689
Bobée, B.; Robitaille, 1975: Correction of bias in the estimation of the coefficient of skewness. Water Resources Research 11(6), 851–854
Bobée, B.; Robitaille, 1977: The use of Pearson type 3 and log-Pearson type 3 distributions revisited. Water Resources Research 13(2), 427–443
Cunnane, C., 1987: Review of statistical models for flood frequency estimation. Proceedings of the International Symposium on Flood Frequency and Risk Analyses, pp. 49–95, D. Reidel Publishing Company
Greenwood, J.A.; Landwehr, J.M.; Matalas, N.C.; Wallis, J.R. 1979: Probability weighted moments: definition and relation to parameters of several distributions expressible in inverse form. Water Resources Research 15(5), 1049–1054
Hosking, J.R.M. 1989: L-Moments: Analysis and evaluation of distribution using linear combinations of order statistics. Journal of the Royal Statistical Society, Series B, 51
Houghton, J.C. 1978: The incomplete means estimation procedure applied to flood frequency analysis. Water Resources Research 14(6), 1111–1115
Himmelblau, D.M. 1972: Applied nonlinear programming. McGraw-Hill Book Co., New York
Jain, D. 1986: A comparative evaluation of methods of flood frequency analysis and estimation of parameters. Unpublished M.S. thesis, Louisiana State University, Baton Rouge, Louisiana
Kite, G.W. 1978: Frequency and risk analysis in hydrology. Water Resources Publications, P.O. Box 303, Fort Collins, CO 80522
Kuczera, G. 1982: Robust flood frequency models. Water Resources Research 18(2), 315–324
Matalas, N.C.; Wallis, J.R. 1973: Eureka! It fits a Pearson type 3 distribution. Water Resources Research 9(2), 281–289
Naghavi, B.; Singh, V.P.; Yu, F.X. 1991: LADOTD 24-hour rainfall frequency maps and I-D-F curves. Louisiana Transportation Research Center, LTRC Report No. 263, Baton Rouge, LA
Naghavi, B.; Yu, F.X. 1993a: Flood frequency analysis using optimization techniques. Louisiana Transportation Research Center, LTRC Report No. 249, Baton Rouge, LA
Naghavi, B.; Yu, F.X.; Singh, V.P. 1993b: Comparative evaluation of frequency distributions for Louisiana extreme rainfall. Water Resources Bulletin 29(2), 211–219
Naghavi, B.; Yu, F.X. 1993: Selection of an estimation method for the LP3 distribution. Water Resources Research, submitted
Press, W.H.; Flannery, B.P.; Teukolsky, S.A.; Vetterling, W.T. 1986: Numerical recipes. Cambridge University Press, London
Rao, D.V. 1980a: Log-Pearson type 3 distribution: A generalized evaluation. J. of Hydraulic Engineering, ASCE 106(5), 853–872
Rao, D.V. 1980b: Log Pearson type 3 distribution: method of mixed moments. J. Hydraulic Division, ASCE 106(HY6), 999–1019
U.S. Water Resources Council. 1967: Guidelines for determining flood flow frequency. Water Resources Council Bull. 15, Washington, D.C.
Wallis, J.R.; Wood, E.F. 1985: Relative accuracy of log-Pearson III procedures. J. Hydraulic Div., Proc. ASCE 111(HY7), 1043,1056
Wallis, J.R.; Matalas, N.C.; Slack, J.R. 1974: Just a moment!. Water Resources Research 10(2), 211–219
Yu, F.X.; Singh, V.P. 1993: An efficient and derivative-free algorithm for finding the minimum of a 1-D user-defined function. Advances in Engineering Software 16, 161–169
Yu, F.X.; Li, W.-Q.; Singh, V.P.; Naghavi, B. 1993: Estimating LP3 parameters using a combination of the method of moments and least squares. J. Environmental Hydrology 1(2), 9–19
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Yu, F.X., Naghavi, B., Singh, V.P. et al. MMO: An improved estimator for log-Pearson type-3 distribution. Stochastic Hydrol Hydraul 8, 219–231 (1994). https://doi.org/10.1007/BF01587236
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DOI: https://doi.org/10.1007/BF01587236