Logistic曲线与Gompertz曲线的比较研究  

Comparisons on Logistic Curve and Gompertz Curve

作　　者：朱正元[1] 陈伟侯[2] 陈丰 

机构地区：[1]中央民族大学数学系,北京100081 [2]中国农业大学理学院,北京100094 [3]中国科学院动物研究所,北京100086

出　　处：《数学的实践与认识》2003年第10期66-71,共6页Mathematics in Practice and Theory

基　　金：得到中央民大"十五"科研规划重点项目(30 6 4)基金资助

摘　　要：本文对 Logistic曲线与 Gom pertz曲线的性状进行了研究和对比 ,指出了它们都有使其二阶导数达到最大值、最小值和零值的三个点 ,称为曲线的特征点 .通过对特征点的研究 ,我们提出了三个定理 ,从而断定这两类曲线既有许多相似之处 。The properties of the two curves w er e studied. Unique points of maximum, minimum and null value have been found in t he second derivatives of the two curves, denoted as t 1, t 2 and t 0 respectively, which define the curves and are called critical points. Based on t he comparison of the critical points of the two curves, three theorems were prop osed and have been proved by the author. They exhibit astonishing similarties as well as essential distinctions that could not be ignored. It is always a perple xity for practicians to decide which one of the fitting curves is suitable for a certain set of observed data. Therefore, it is still an unsolved problem to sup ply for practicians a easy-handled measure to make the right choice.

关 键 词：Logistic曲线 Gompertz曲线 性状 特征点 导数 微分方程 

分 类 号：F224.7[经济管理—国民经济]