# 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) |

L | constant (dimensionless) |

e | e |

k | constant (dimensionless) |

x | variable (in the range of real numbers from −∞ to +∞) (dimensionless) |

x_{0} | constant (dimensionless) |