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The Analysis and Improvement of the Fuzzy Weighted Optimum Curve-Fitting Method of Pearson – Type III Distribution

Author

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  • Guan-Jun Lei

    (State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin)

  • Jun-Xian Yin

    (State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin)

  • Wen-Chuan Wang

    (North China University of Water Resources and Electric Power)

  • Hao Wang

    (State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin)

Abstract

In the optimum curve-fitting method, due to the dissimilar purposes, the discrepant accuracy and positions of the experience points, the importance of the points should be different. For the limited sample size of the hydrologic sequence, there are sampling errors in the parameter estimation. In order to focus on the important points and reduce the errors effectively, the weight has been introduced in the optimum curve-fitting method. The existing weighted optimum curve-fitting methods are analyzed and studied. The Fuzzy Weighted Optimum Curve-fitting Method (FWOCM), which are the limited nomograph length and the determination of the membership degree function without the premise of a large sample. In order to solve the problems, the improvement of the method should be conducted. A new membership degree function is deducted and demonstrated on the premise that the hydrologic sequence is a large sample. The Monte Carlo statistical test optimum curve-fitting method is used to extend the nomograph to the entire frequency range. The improved FWOCMs are tested by the ideal data and the real data. In order to evaluate the performances of the improved FWOCMs, the selected excellent method and the improved percentage method are introduced to analyze the relative errors. The results show that the extension of the nomograph and the new membership degree function to a certain extent weakens the impact of the shorter hydrologic sequence on the curve-fitting. It indicates that the effect of the improved optimum curve-fitting methods is satisfying and can be used in the engineering practice.

Suggested Citation

  • Guan-Jun Lei & Jun-Xian Yin & Wen-Chuan Wang & Hao Wang, 2018. "The Analysis and Improvement of the Fuzzy Weighted Optimum Curve-Fitting Method of Pearson – Type III Distribution," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 32(14), pages 4511-4526, November.
    • Handle: RePEc:spr:waterr:v:32:y:2018:i:14:d:10.1007_s11269-018-2055-9
    DOI: 10.1007/s11269-018-2055-9
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    References listed on IDEAS

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    1. Karvanen, Juha & Nuutinen, Arto, 2008. "Characterizing the generalized lambda distribution by L-moments," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 1971-1983, January.
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    Cited by:

    1. Muhammad Shafeeq ul Rehman Khan & Zamir Hussain & Ishfaq Ahmad, 2021. "Effects of L-Moments, Maximum Likelihood and Maximum Product of Spacing Estimation Methods in Using Pearson Type-3 Distribution for Modeling Extreme Values," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 35(5), pages 1415-1431, March.
    2. Kai Wang & Shaojie Zhang, 2021. "Rainfall-induced landslides assessment in the Fengjie County, Three-Gorge reservoir area, China," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 108(1), pages 451-478, August.
    3. Hanlin Li & Longxia Qian & Jianhong Yang & Suzhen Dang & Mei Hong, 2023. "Parameter Estimation for Univariate Hydrological Distribution Using Improved Bootstrap with Small Samples," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 37(3), pages 1055-1082, February.

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