Abstract
Most of the existing plotting position formulas have been proposed for use in the analysis of systematic flood records, but little has been reported on the plotting formulas for historical or non-systematic flood samples. In particular, no previous investigations have specifically examined the probability plots for the Pearson type III (P3) distribution in the analysis of historical flood information. The present paper suggests a new plotting position formula for the P3 distribution for use with both systematic and historical flood records. The proposed formula has a simple structure as do most existing formulas, but it is more flexible because in can take explicitly into account the skewness coefficient of the underlying distribution. Further, results of graphical and numerical comparisons have demonstrated that the suggested formula provided the least bias in flood quantile estimation as compared with many available plotting formulas, including the well-known Weibull formula. Finally, results of a numerical example using actual flood data have indicated the practica convenience of the proposed plotting formula. It can be concluded that the formula developed in this study is the most appropriate for the P3 distribution in the analysis of flood records considering historical information.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
AdmowskiK.: 1981, ‘Plotting Position Formula for Flood Frequency’, Water Resour. Bulletin, 7(2), 197–201.
ArnellN. W., BeranM., and HoskingJ. R. M.: 1986, ‘Unbiased Plotting Position for the General Extreme Value Distribution’. J. Hydrol., 86, 59–69.
BobeeB., and RobitailleR.: 1977, ‘The Use of the Pearson Type 3 and Log Pearson Type 3 Distributions Revisited’, Water Resour. REs., 13(2), 427–443.
BlomG.: 1958, Statistical Estimates and Transformed Beta-Variable, John Wiley and Sons, New York, N. Y.
CondieR. and LeeK.: 1982, ‘Flood Frequency Analysis with Historic Information’, J. Hydrol. 58, 47–61.
CunnaneC.: 1978, ‘Unbiased Plotting Positions-A Review’, J. Hydrol., 37, 205–222.
GringortenI. I.: 1963, ‘A Plotting Rule for Extreme Probability Paper’, J. Geophys. Res., 68(3), 813–814.
Guang-YanJ.: 1987, ‘Problem is Statistical Treatment of Flood Series’, J. Hydrol., 96, 173–184.
GumbelE. J.: 1943, ‘On the Plotting of Flood Discharges’, Trans. Am Geophys. Res., 68(3), 813–814.
HazenA.: 1914, ‘Storage to be Provided in Impounding Reservoirs for Municipal Water Supply’, Trans. Am. Soc. Civ. Eng., 77, 1547–1550.
HirschR. M.: 1987, ‘Probability Plotting Position Formulas for Flood Records with Historical Information’, J. Hydrol., 96, 185–199.
HirschR. M. and StedingerJ. R.: 1987, ‘Plotting Positions for Historical Floods and their Precision’, Water Resour. Res. 23(4), 715–727.
In-naN., and NguyenV. T. V.: 1989, ‘An Unbiased Plotting Position Formula for the General Extreme Value Distribution’, J. Hydrol., 106, 193–209.
JinM. and StedingerJ. R.: 1989, ‘Flood Frequency Analysis with Regional and Historical Information’, Water Resour. Res., 25(5), 925–936.
KimballF.: 1960, ‘On the Choice of Plotting Positions on Probability Paper’, J. Am. Stat. Assoc. 55, 546–560.
NguyenV. T. V., In-naN., and BobeeB.: 1989, ‘New Plotting Position Formula for Pearson Type III Distribution’, J. Hydraul. Eng., ASCE, 115(6), 709–730.
Shi-QianH.: 1987, ‘A General Survey of Flood-Frequency Analysis in China’, J. Hydrol., 96, 15–25.
StedingerJ. R., and cohnT.: 1986, ‘Flood Frequency Analysis with Historical and Paleoflood Information’, Water Resour. Res. 22(5), 785–793.
SutcliffeJ. V.: 1987, ‘The Use of Historical Records in Flood Frequency Analysis’, J. Hydrol. 96, 159–171.
ThomasW. O.Jr.: 1985, ‘A Uniform Technique for Flood Frequency Analysis’, J. Water Resour. Plan. and Man., 111(3), 321–337.
UNESCO: 1987, Casebook of Methods for Computing Hydrological Parameters for Water Projects, Paris, France.
WeibullW.: 1939, ‘A Statistical Theory of Strength of Materials’, Ing. Vet. Ak. Handl., 151, Generalstabens Litografiska Anstals Forlag, Stockholm, Sweden.
XuewuJ., JingD., ShenH. W., and SalasJ. D.: 1984, ‘Probability Plots for Pearson Type III Distribution’, J. Hydrol. 74, 1–29.
ZhangY.: 1982, ‘Plotting Positions of Annual Flood Extremes Considering Extraordinary Values’, Water Resour. Res., 18(4), 859–864.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Van Nguyen, TV., In-Na, N. Plotting formula for pearson type III distribution considering historical information. Environ Monit Assess 23, 137–152 (1992). https://doi.org/10.1007/BF00406958
Issue Date:
DOI: https://doi.org/10.1007/BF00406958