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

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.