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Improved fuzzy weighted optimum curve-fitting method for estimating the parameters of a Pearson Type-III distribution

ABSTRACT The objective of the curve-fitting method is to determine the optimal distribution by parameter estimation. The selection of the parameter estimation methods and the determination of the parameter estimation results may vary according to the different aims of the curve fitting, as well as the different accuracies and positions of the points. To solve the problem, the fuzzy weighted optimum curve-fitting method (FWOCM) was used to deal with the characters. The deficiencies of the original FWOCM were analysed, and it was found that the membership function and nomograph were unable to effectively deal with the curve fitting. An improved method and its indexes were evaluated, using effectiveness and unbiasedness as the assessment criteria, while scoring and percentage methods were chosen to comprehensively assess the statistical results. Compared with FWOCM, the results showed greater effectiveness and unbiasedness in the improved method.