Logistic function - Wikipedia, the free encyclopedia
The function was named in 1844-1845 by Pierre François Verhulst, who studied it in relation to population growth.[2] The initial stage of growth is approximately exponential; then, as saturation begins, the growth slows, and at maturity, growth stops.
A logistic function or logistic curve is a common "S" shape (sigmoid curve), with equation:
where e is the natural logarithm base (also known as Euler's number).[1] For values of x in the range of real numbers from −∞ to +∞, the S-curve shown on the right is obtained.
The function was named in 1844-1845 by Pierre François Verhulst, who studied it in relation to population growth.[2] The initial stage of growth is approximately exponential; then, as saturation begins, the growth slows, and at maturity, growth stops.
In practice, due to the nature of the exponential function e−x, it is often sufficient to compute x over a small range of real numbers such as [−6, +6].
is an
逻辑函数或逻辑曲线是一种常见的S形函数，它是皮埃尔·弗朗索瓦·韦吕勒在1844或1845年在研究它与人口增长的关系时命名的。广义Logistic曲线可以模仿一些情况人口增长（P）的S形曲线。起初阶段大致是指数增长；然后随着开始变得饱和，增加变慢；最后，达到成熟时增加停止。
一个简单的Logistic函数可用下式表示：
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