Logistic曲线方程的解析与拟合优度测验

Analysis and Making Good Fitting Degree Test for Logistic Curve Regression Equation

为充分利用Logistic曲线的载荷信息,通过Logistic曲线生长过程速度函数的一阶和二阶导数,得到了Logistic曲线增长或生长过程的始盛期、高峰期、盛末期的分点分别为:t1=(lna-1 317)/b,t2=(lna)/b,t3=(lna+1 317)/b。也可用速度函数的两个拐点将Logistic曲线的生长过程分为渐增期(t=0～(lna-1 317)/b)、快增期(t=(lna-1 317)/b～(lna+1 317)/b)、缓增期(t=(lna+1 317)/b)～∞)。提出采用适合性x2测验,进行Logistic曲线回归方程拟合优度测验。并进行了实例分析和讨论。

To make full use of the information of Logistic curve we obtained the cut points:beginning fast growth period,the fastest growth period,lowest growth period were t1=(lna-1.317)/b,t2=(lna)/b,t3=(lna+1.317)/b,by first and second derivative of velocity function of increasing or growth process of logistic curve. And using two yieding point of the velocity function,the increasing or growth process of Logistic curve was divided into gradually growth period (t=0～(lna-1.317)/b)、fast growth period(t=(lna-1.317)/b～(lna+1.317)/b)、solw growth period(t=(lna+1.317)/b)～∞).for fitting a good Logistic curve regression equation the adopting x^2 test was recommended. And a living example was analyzed and discussed.