高斯牛顿法在皮尔逊Ⅲ型曲线适线中的应用

摘要

Pearson Type Ⅲcurve is commonly used in infrequency computation of hydrology in China,but the precise estimate of the parameters is still a difficulty. This paper used Gauss-Newton method on Pearson Type Ⅲ curve to estimate the parameters,based on the basic ideas of least squares in the complex nonlinear fitting,through the absolute standards,square and criterion and expectation formula. It was automatically to a-chieve the optimal line on Pearson TypeⅢand to seek the best curve ! fitting results by using the Matlab 2013a software. The results show that Gauss-Newton method has better fitting effect in the estimate of the parameter.%皮尔逊Ⅲ型曲线是水文频率计算的常用曲线，其参数的精确估计是一个难点。基于复杂非线性拟合的最小二乘法基本思想，通过绝对值准则、平方和准则和期望值公式，采用高斯牛顿法对皮尔逊Ⅲ型曲线进行参数估计，通过matlab 2013a软件编程，实现皮尔逊Ⅲ型曲线的自动优化适线，寻求最优适线结果。实例应用结果表明高斯牛顿法参数估计有较好的拟合效果。