\[y = \frac{a}{1+e^{-bx}}\]
Variables
yfunction value
aupper limit value
bgrowth steepness constant
xindependent variable
Description
What is this formula?
This formula represents a sigmoid function, an S-shaped curve commonly used to model smooth transitions between two states.
When to use it
Use this formula when modeling gradual activation, saturation effects or bounded growth processes.
Example
For:
a=1
b=2
x=1
y=1/(1+(℮^(-2*1)))
y≈0.881
Applications
Artificial neural networks
Machine learning
Population models
Control systems
Biological processes
Probability models