Читать книгу Numerical Methods in Computational Finance - Daniel J. Duffy - Страница 57

A logistic function (or logistic curve) is an S-shaped sigmoid curve defined by the equation:

(3.15)

where

-value of sigmoid's midpoint

curve's maximum value

steepness of the curve.

A special case is when , resulting in the standard logistic function defined by the equation:

We can verify from this equation that the logistic function satisfies the non-linear initial value problem:

(3.16)

The logistic function models processes in a range of fields such as artificial neural networks (learning algorithms, where it is called an activation function), economics, probability and statistics, to name a few.