Sigmoid Function

A sigmoid function is a mathematical function having an "S" shape (sigmoid curve). Often, sigmoid function refers to the special case of the logistic function shown at right and defined by the formula

Another example is the Gompertz curve. It is used in modeling systems that saturate at large values of t. Another example is the ogee curve as used in the spillway of some dams. A wide variety of sigmoid functions have been used as the activation function of artificial neurons, including the logistic and hyperbolic tangent functions. Sigmoid curves are also common in statistics as cumulative distribution functions, such as the integrals of the logistic distribution, the normal distribution, and Student's t probability density functions.