Abstract
The log-Pearson type 3 (LP3) distribution has been one of the most frequently used distributions for hydrologic frequency analyses since the recommendation of the Water Resources Council (1967, 1982) of the United States as to its use as the base method. The Water Resources Council also recommended that this distribution be fitted to sample data by using mean, standard deviation and coefficient of skewness of the logarithms of flow data [i.e., the method of moments (MOM)]. A large volume of literature on the LP3 distribution has since been published with regard to its accuracy and methods of fitting or parameter estimation. McMahon and Srikanthan (1981) and Srikanthan and McMahon (1981) examined the applicability of LP3 distribution to Australian rivers and questioned the assumption of setting to zero the coefficient of skewness of logarithms of peak discharges that were not statistically different from zero. They evaluated the effect of sample size, distribution parameters and dependence on peak annual flood estimates. Gupta and Deshpande (1974) applied LP3 distribution to evaluate design earthquake magnitudes. Phien and Jivajirajah (1984) applied LP3 distribution to annual maximum rainfall, annual streamflow and annual rainfall. Wallis and Wood (1985) found, based on Monte Carlo experiments, that the flood quantile estimates obtained by using an index flood type approach with either a generalized extreme value distribution or a Wakeby distribution fitted by PWM were superior to those obtained by LP3 distribution with MOM -based parameters. This finding was challenged later by several investigators (Beard, 1986; Landwehr et al., 1986).
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References
Arora, K. and Singh, V.P., 1987a. A comparative evaluation of the estimators of commonly used flood frequency models: 1. Monte Carlo simulation. Completion Report, Louisiana Water Resources Research Institute, Louisiana State University, Baton Rouge, Louisiana.
Arora, K. and Singh, V.P., 1987b. A comparative evaluation of the estimators of commonly used flood frequency models: 2. Computer programs. Completion Report, Louisiana Water Resources Research Institute, Louisiana State University, Baton Rouge, Louisiana.
Arora, K. and Singh, V.P., 1988. On the method of maximum likelihood estimation for log-Pearson type 3 distribution. Stochastic Hydrology and Hydraulics, Vol. 2, No. 2, pp. 156–160.
Arora, K. and Singh, V.P., 1989a. A comparative evaluation of the estimators of the log Pearson type (LP) 3 distribution. Journal of Hydrology, Vol. 105, pp. 9–37.
Arora, K. and Singh, V.P., 1989b. A note on the mixed moment estimation for the log-Pearson type 3 distribution. Journal of the Institution of Engineers (India), Civil Engineering Division, Vol. 69, Part C15, pp. 298–301.
Ashkar, F. and Bobee, B., 1987. The generalized method of moments as applied to problems of flood frequency analysis: Some practical results for the log-Pearson type 3 distribution. Journal of Hydrology, Vol. 90, pp. 199–217.
Ashkar, F. and Bobee, B., 1988. Confidence intervals for flood events under a Pearson 3 or log Pearson 3 distribution. Water Resources Bulletin, Vol. 24, No. 3, pp. 639–650.
Beard, L.R., 1986. Comment on “Relative accuracy of log Pearson III procedures by J.R. Wallis and E.F. Wood.” Journal of Hydraulic Engineering, Vol. 112, pp. 1205–1206.
Benson, M.A., 1968. Uniform flood-frequency estimating methods for federal agencies. Water Resources Research, Vol. 4, No. 5, pp. 891–908.
Bobee, B., 1975. The log Pearson type 3 distribution and its application in hydrology. Water Resources Research, Vol. 11, No. 5, pp. 681–689.
Bobee, B. and Ashkar, F., 1988. Generalized method of moments applied to LP3 distribution. Journal of Hydraulic Engineering, Vol. 114, N. 8, pp. 899–909.
Bobee, B. and Ashkar, F., 1991. The Gamma Family and Derived Distribution Applied in Hydrology. Water Resources Publications, Littleton, Colorado.
Bobee, B., Cavadias, G., Ashkar, F., Bernier, J. And Rasmussen, P., 1993. Towards a systematic approach to comparing distributions used in flood frequency analysis. Journal of Hydrology, Vol. 142, pp. 121–136.
Bobee, B. and Robitaille, R., 1975. Correction of bias in the estimation of the coefficient of skewness. Water Resources Research, Vol. 11, No. 6, pp. 851–854.
Cohen, T.A., Lane, W.L. and Baier, W.G., 1997. An algorithm for computing moments-based flood quantile estimates when historical flood information is available. Water Resources Research, Vol. 33, No. 9, pp. 2089–2096.
Condie, R., 1977. The log Pearson type 3 distribution: The T-year event and its asymptotic standard method by maximum likelihood theory. Water Resources Research, Vol. 13, pp. 987–991.
Gupta, I.D. and Deshpande, V.C., 1994. Appliation of log-Pearson type-Ili distribution for evaluating design earthquake magnitudes. Journal of the Institution of Engineers (India), Civil Engineering Division, Vol. 75, pp. 129–134.
Haktanir, T., 1991. Statistical modelling of annual maximum flows in Turkish rivers. Hydrological Sciences Journal, Vol. 36, No. 4, pp. 367–389.
Hoshi, K. And Burges, S.J., 1981a. Approximate estimation of the derivative of a standard gamma quantile for use in cinfidence interval estimates. Journal of Hydrology, Vol. 53, pp. 317–325.
Hoshi, K. and Burges, S.J., 198 lb. Sampling properties of parameter estimates for the log Pearson type 3 distribution using moments in real space. Journal of Hydrology, Vol. 53, pp. 305–316.
Kite, G.F. 1978. Frequency and Risk Analyses in Hydrology. Water Resources Publications, Littleton, Colorado.
Kuczera, G., 1982a. Combining site-specific and regional information: An empirical Bayes approach. Water Resources Research, Vol. 18, No. 2, pp. 306–314.
Kuczera, G., 1982b. Robust flood frequency models. Water Resources Research, Vol. 18, No. 2, pp. 315–324.
Landwehr, J.M., Matals, N.C. and Wallis, J.R., 1978. Some comparison of flood statistics in real and log space. Water Resources Research, Vol. 14, No. 5, pp. 902–920.
Landwehr, J.M., Tasker, G.D. and Jarret, R.D., 1986. Comment on “Relative accuracy of log Pearson III procedures by J.R. Wallis and E.F. Wood.” Journal of Hydraulic Engineering, Vol. 112, pp. 1206–1210.
Loganathan, G.V., Mattejat, P., Kuo, C.Y. and Diskin, M.H., 1986. Frequency analysis of low flows: Hypothetical distribution methods and a physically based approach. Nordic Hydrology, Vol. 17, pp. 129–150.
McMahon, T.A. and Srikanthan, R., 1981. Log Pearson III distribution-Is it applicable to flod frequency analysis of Australian streams? Journal of Hydrology, Vol. 52, pp. 139–147.
Nozdryn-Plotinicki, M.J. and Watt, W.E., 1979. Assessment of fitting techniques for the log Pearson type 3 distribution using Monte Carlo simulation. Water Resources Research, Vol. 15, No. 3, pp. 714–718.
Oberg, K.A. and Mades, D.M., 1987. Estimating generalized skew of the log-Pearson type III distribution. Water Resources Investigations Report 86–4009, 42 pp., U.S. Geological Survey, Urbana, Illinois.
Ouarda, T.B.M. and Ashkar, F., 1998. Effect of trimming on LP III flood quantile estimates. Journal of Hydrologic Engineering, Vol. 3, No. 1, pp. 33–42.
Phien, H.N. and Hira, M.A., 1983. Log Pearson type-3 distribution: Parameter Estimation. Journal of Hydrology, Vol. 64, pp. 25–37.
Phien, H.N. and Hsu, L.C., 1985. Variance of the T-year event in the log Pearson type 3 distribution. Journal of Hydrology, Vol. 77, pp. 141–158.
Phien, H.N. and Jivajirajah, T., 1984. Application of the log Pearson type-3 distribution in hydrology. Journal of Hydrology, Vol. 73, pp. 359–372.
Pilon, P.J. and Adamowski, K., 1993. Asymptotic variance of flood quantile in log Pearson type III distribution with historical information. Journal of Hydrology, Vol. 143, pp. 481–503.
Rao, D.V., 1980a. Log Pearson type 3 distribution: Method of mixed moments. Journal of Hydraulics Division, ASCE, Vol. 106, No. HY6, pp. 999–1019.
Rao, D.V., 1980b. Log Pearson type 3 distribution: A generalized evaluation. Journal of Hydraulics Division, ASCE, Vol. 106, No. HY5, pp. 853–872.
Rao, D.V., 1981. Three-parameter probability distribution. Journal of Hydraulics Division, ASCE, Vol. 107, No. HY3, pp. 339–358.
Rao, D.V., 1983a. Estimating log Pearson parameters by mixed moments. Journal of Hydraulic Engineering, Vol. 109, No. 8, pp. 1118–1132.
Rao, D.V., 1983b. Three-parameter probability distributions. Journal of the Hydraulics Division, ASCE, Vol. 107, No. HY3, pp. 339–357.
Rao, D. V., 1988. Estimating extreme events: Log Pearson type 3 distribution. Chapter 9 in Civil Engineering Practice: Water Resources and Environmental Management, edited by P.N. Cheremisinoff, N.C. Cheremisinoff and S.L. Cheng, Vol. 5, pp. 291–304, Technomic Publishing Company, Inc., Lancaster, Basel.
Reich, B.M., 1970. Flood series compared to rainfall extremes. Water Resources Research, Vol. 6, No. 6, pp. 1655–1667.
Rossi, F., Fiorentino, M. and Versace, P., 1984. Two-component extreme value distribution for flood frequency analysis. Water Resources Research, Vol. 20, pp. 847–856.
Shen, H.W., Bryson, M.C. and Ochoa, I.D., 1980. Effect of tail behavior assumptions on flood predictions. Water Resources Research, Vol. 16, No. 2, pp. 361–364.
Singh, V.P. and Singh, K., 1988. Parameter estimation for log-Pearson type III distribution by POME. Journal of Hydraulic Engineering, Vol. 114, No. 1, pp. 112–122.
Song, D. and Ding, J., 1988. The application of probability weighted moments in estimating the parameters of the Pearson type three distribution. Journal of Hydrology, Vol. 101, pp. 47–61.
Srikanthan, R. and McMahon, T.A., 1981. Log Pearson III distribution-Effect of dependence, distribution parameters and sample size on peak annual flood estimates. Journal of Hydrology, Vol. 52, pp. 149–159.
Tasker, G.D., 1987. A comparison of methods for estimating low flow characteristics of streams. Water Resources Bulletin, Vol. 23, No. 6, pp. 1077–1083.
Tung, K.T. and Mays, L.W., 1981. Generalized skew coefficients for flood frequency analysis. Water Resources Bulletin, Vol. 17, No. 2, pp. 262–269.
Vogel, R.M., Thomas, W.O. and McMahon, T.A., 1992. Flood-flow frequency model selection in southwestern United States. Journal of Water Resources Planning and Management, Vol. 119, No. 3, pp. 353–366.
Wallis, J.R. and Wood, E.F., 1985. Relative accuracy of log Pearson III procedures. Journal of Hydraulic Engineering, Vol. 111, No. 7, pp. 1043–1056.
Water Resources Council, 1967. A uniform technique for determining flood flow frequencies. Bulletin No. 15, 15 pp., Washington, D.C.
Water Resources Council, 1982. Guidelines for determining flood flow frequency. Bulletin 17 B, Hydrology Subcommittee, Interagency Advisory Committee on Water Data, Washington, D.C.
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Singh, V.P. (1998). Log-Pearson Type III Distribution. In: Entropy-Based Parameter Estimation in Hydrology. Water Science and Technology Library, vol 30. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1431-0_15
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