灰色理论在logistic曲线拟合中的应用

The Application of Grey Theory to Logistic Curve Fitting

本文应用灰色理论中灰导数拓扑空间的定理和非线性灰色建模的方法,直接按最小二乘法求解logistic曲线的参数,对曲线进行灰色法拟合,并与加权拟合法进行了对比。结果两种拟合方法的差异经F检验,无统计学意义。因应用灰色理论拟合计算简单,对样本容量及概率分布没有严格的要求,且拟合精度较高,用来拟合logistic曲线不失为一种值得推广应用的新方法。

In this paper, it quotes those theorems concerned of grey control theory which Mr Deng Julong has founded, according to method of least squares to calculate the parameter of logistic curve, dealt with by grey fitting and compared it with weighted fitting. Through F test,the result shows that the difference between two kinds of fitting methods is non-statistical significance.Because of its simple calculation, no strict demand on sample content and probit distribution, as well as its higher precision, grey fitting method is proved to be a deserving widely used new method to fit logistic curve.