Gompertz模型和Logistic模型的拟合

常见的三参数 S形生长模型有 Gompertz模型和 L ogistic模型 .它们在拐点处的坐标、导数与它们的参数是能够相互唯一确定的 .当利用拟事隐函数曲线的 GNL 法对这两种模型进行最小二乘拟合时 ,可根据这一性质对单个未线性化参数的初始值进行搜索 .有时也可对该初始值直接进行搜索 .最后以几个实例成功地对这种算法进行了验证

Fitting Gompertz Model and Logistic Model

The common growth models with three parameters in the shape of S are Gompertz and Logistic. The coordinates and diff erential coefficients of their inflection points and their parameters can be uni quely determined each other. According to this property, the initial values of t heir single non-linearized parameters can be searched during the models are fit ted in the meaning of least square by means of GNL method which can fit the curv e of implicit function. Sometimes the initial values can be dirctly searched. An d it is successful to test and verify this algorithm in several examples.