Abstract
Risk can be estimated by the probability of exceedance of XT (flow with return period T). An accurate determination of XT with its confidence intervals is important in this context. We will consider estimation of XT using several methods in the case of the Pearson type 3 and log Pearson type 3 distributions.
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References
Ashkar F. and B. Bobée (1986) Comment on: Variance of the T - Year event in the Log-Pearson Type 3 distribution. Journal of Hydrology, 84(1): 181–187.
Beard L.R. (1962) Statistical Methods in Hydrology. Civil Works Investigation Project CW–151, US Army Corps of Engineers, Sacramento, California. 62 p. 2 appendices.
Benson M.A. (1968) Uniform flood–frequency estimating methods for federal agencies. Wat. Res. Res. 4(5): 891–908.
Bobée B. (1973) Sample error of T year events computed by fitting a Pearson Type 3 distribution. Wat. Res. Res. 9(5): 1264–1270.
Bobée B. (1975a) The Log–Pearson Type 3 distribution and its application in hydrology. Wat. Res. Res. 11(5): 681–689.
Bobée B. (1975b) Etude des propriétés mathématiques et statistiques des lois Pearson type 3 et log Pearson type 3. INRS–Eau, rapport scientifique no. 55, 175p.
Bobée B. and F. Ashkar (1988a) The generalized method of moments applied to the log–Pearson type 3 distribution. Journal of Hydraulic Engineering, ASCE, 114(8): 899–909.
Bobée B. and F. Ashkar (1988b) Sundry Averages Method for estimating parameters of the Log–Pearson type 3 distribution. INRS-Eau, rapport scientifique No. 251.
Bobée B. and F. Ashkar (1991) The gamma family and derived distributions applied in hydrology, 200 p. Water Resources Publications, Fort Collins, Colorado.
Bobée B. and P. Boucher (1981) Calcul de la variance d’ un événement de période de retour T: cas des lois Log–Pearson type 3 et Log Gamma ajustées par la méthode des moments sur la série des valeurs observées, INRS–Eau, rapport scientifique no. 135, 17 p.
Bobée B. and L. Desgroseilliers (1985) Ajustement des distributions Pearson Type 3, Gamma, Gamma Généralisée et Log Pearson. INRS–Eau, rapport scientifique no. 105, 63 p.
Bobée B. and R. Robitaille (1975) Correction of bias in the estimation of the coefficient of skewness. Wat. Res. Res. 11 (6): 851–854.
Fisher R.A. (1921) On the mathematical foundations of theoretical statistics. Roy. Soc. of London Phil. Trans. Ser. A, 222: 309–368.
Hazen A. (1924) Discussion on “Theoretical Frequency Curves” by Foster. Transactions ASCE 87:174–179.
Hoshi K. and U. Leeyavanija (1986) A new approach to parameter estimations of gamma type distributions. Journal of Hydrosciences and hydraulic engineering, 79–95.
I.E.A. (1977) Australian rainfall and runoff flood analysis and design. Institute of engineers, Australia Camberra, A.C.T., 149 p.
Kirby W. (1974) Algebraic boundedness of sample statistics. Wat. Res. Res. 10(2):220–222.
Landwehr J.M., Matalas N.C. and J.R. Wallis (1978) Some comparisons of flood statisties in real and log space. Wat. Res. Res. 14 (5):902–920.
Pearson K. (1895) Contributions of the mathematical theory of evolution. Philosophical Transactions of the Royal Society of London Series A 186, 343–414.
Rao D.V. (1980) Log–Pearson type 3 distribution: method of mixed moments, ASCE, Journal of Hydraulics division, 106(6):999–1019.
Rao D.V. (1983) Estimating Log–Pearson parameters by mixed moments. ASCE, Journal of Hydraulics division, 109 (8):1119–1 132.
Wallis J.R., Matalas N.C. and J.R. Slack (1974) Just a moment. Wat. Res. Res., 10 (2):211–219.
WRC (1976) Guidelines for determining flood flow frequency. US Water Resources Council hydrology Commettee, Washington, D.C.
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© 1991 Springer-Verlag Berlin Heidelberg
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Bobée, B., Ashkar, F., Roy, R., Perreault, L. (1991). Risk Analysis of Hydrological Data Using Gamma Family and Derived Distributions. In: Ganoulis, J. (eds) Water Resources Engineering Risk Assessment. NATO ASI Series, vol 29. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-76971-9_2
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DOI: https://doi.org/10.1007/978-3-642-76971-9_2
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