Logistic function

https://arbital.com/p/logistic_function

by Joe Zeng Jul 7 2016

A monotonic function from the real numbers to the open unit interval.


[summary: The logistic function is a [-sigmoid] function that maps the real numbers to the unit interval $~$(0, 1)$~$ using the formula $~$\displaystyle f(x) = \frac{1}{1 + e^{-x}}$~$ or variants of this formula.]

The logistic function is a [-sigmoid] function that maps the real numbers to the unit interval $~$(0, 1)$~$ using the formula $~$\displaystyle f(x) = \frac{1}{1 + e^{-x}}$~$.

More generally, there exists a [family_of_functions family] of logistic functions that can be written as $~$\displaystyle f(x) = \frac{M}{1 + \alpha^{c(x_0 - x)}}$~$, where:

Applications