Logistic曲线拟合方法研究

Study on the fitting methods of logistic curve

Logistic模型具有广泛的实用性。本文推导了用三点法估计该模型中参数K值的公式 ,并提出了估计K值的新方法一四点法和拐点法。用 3种方法求出K值后 ,再用线性化回归获得另外两个参数a、r,应用实例研究表明 :3种方法都可得到较高拟合精度 ,其中以四点法最优。而且 ,以这些方法得到的参数估计值作为初始值进行非线性回归 ,易获得 3个参数的最优估计。

Logistic curve has far-ranging practicability. The formula estimating parameter K of the model with 3-point method was deduced. In this paper, the other two new methods estimating K value of the Logistic curve equation, 4-point method and yielding point method were put forward. After K value was evaluated, the other two coefficients a, r were estimated with linear regression. With two quoted examples discussed, the results indicated that three methods estimating K value all make good fitting precision, especially 4-point method best. Moreover, Nonlinear regression applying above-mentioned estimate values of K, a, r as starting points, easily gives these coefficients best evaluation.