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

Sooyoung Kim, Hongjoon Shin, Hyunjun Ahn, Jun-Haeng Heo

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)471-481
Number of pages11
JournalJournal of Hydrology
Volume527
DOIs
Publication statusPublished - 2015 Aug 1

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skewness
logistics
genetic algorithm
rainfall
distribution
parameter

All Science Journal Classification (ASJC) codes

  • Water Science and Technology

Cite this

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abstract = "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.",
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Development of an unbiased plotting position formula considering the coefficient of skewness for the generalized logistic distribution. / Kim, Sooyoung; Shin, Hongjoon; Ahn, Hyunjun; Heo, Jun-Haeng.

In: Journal of Hydrology, Vol. 527, 01.08.2015, p. 471-481.

Research output: Contribution to journalArticle

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