Morgan-Mercer-Flodin模型和Weibull模型的拟合

Morgan-Mercer-Flodin模型和 Weibull模型是两个著名的四参数 S形生长模型 .在一定的正则变换下 ,它们的隐函数方程及未线性化参数与拐点特征之间的联系都非常相似 .从而可用完全相同的方法对它们的未线性化参数初始值进行搜索 ,以拟合隐函数曲线的 GNL法对它们进行最小二乘拟合 .还用实例对这种算法进行了验证 .

Fitting Morgan-Mercer-Flodin Model and Weibull Model

Morgan-Mercer-Flodin Model and Weibull Model are two famous growth models with four parameters in the shape of S. Under the specific regular transformation, their equations in implicit function form and the relations between their non-linearized parameters and the characters of their inflection points are so similar that the initial values of their non-linearized parameters can be searched just the same. Then the models can be fitted in the meaning of least square by means of GNL method which can fit the curve of implicit function. Several examples are given to test and verify this algorithm.