Development of an unbiased plotting position formula considering the coefficient of skewness for the generalized logistic distribution

Abstract

Summary This study considered the plotting position formula with a coefficient of skewness for the generalized logistic distribution. For the development of the plotting position formula, the theoretical reduced variates were derived with consideration of the shape parameter of the generalized logistic distribution. The parameters of the plotting position formula were estimated using genetic algorithms. The accuracy of derived plotting position formula was examined using the error values between the theoretical and the calculated reduced variates from the derived and existing formulas. The error values from the derived plotting position formula were smaller than those from the existing formulas for - 0.30 ⩽ β - 0.05 and + 0.05 β ⩽ + 0.30 . For - 0.05 ⩽ β ⩽ + 0.05 , the error values from Gringorten’s plotting position formula were smaller than those of other methods, but the differences were notably small, i.e., 0.0001–0.0008. As a result, the derived plotting position formula could be applied to the generalized logistic distribution with a shape parameter range of - 0.30 ⩽ β ⩽ + 0.30 . In addition, the theoretical reduced variate shows a straighter line for sample data plotted on probability paper. And then, the coefficients of determination by the derived plotting position formula were higher than those by Gringorten’s one for applied annual maximum rainfall data in Korea. Therefore, more reliable quantiles can be estimated using the derived plotting position formula.