General Logistic Sigmoid Function

Description

A logistic function or logistic curve is a common “S” shape (sigmoid curve). Data that follows an increasing logistic curve usually describes constrained growth or a cumulative quantity. For small values of the independent variable, the increasing logistic function behaves very much like an (increasing) exponential function. A sigmoid function is a bounded differentiable real function that is defined for all real input values and has a positive derivative at each point.

Related formulas

Variables

f(x)logistic function (dimensionless)
Lconstant (dimensionless)
ee
kconstant (dimensionless)
xvariable (in the range of real numbers from −∞ to +∞) (dimensionless)
x0constant (dimensionless)