A sigmoid function is a mathematical function having a characteristic "S"-shaped curve or sigmoid curve. Often, sigmoid function refers to a special case of the logistic function. It is closely related to the logistic regression.
A sigmoid function looks like this:
$P(Z) = \frac{1}{ 1 + e^{-Z}}$
Other examples of similar shapes include the Gompertz curve (used in modeling systems that saturate at large values of x) and the ogee curve (used in the spillway of some dams). Sigmoid functions have domain of all real numbers, with return value monotonically increasing most often from 0 to 1 or alternatively from −1 to 1, depending on convention.
The sigmoid function is also used in logistic neurons in neural networks. It is useful becauase you can take the derivative for any "z".
The sigmoid cursve is also used for modelling growth of a population in biology.
