The Logistic distribution has density function:

f(x) = (1/b)*

-∞<x<∞, 0<b

where

a |
is the mean of the distribution |

b |
is the scale parameter |

e |
is the base of the natural logarithm, sometimes called Euler's e (2.71...) |

The graphic above shows the shape of the Logistic distribution when the location parameter equals 0 and the scale parameter equals 1, 2, and 3. For a complete listing of all distribution functions, see Distributions and Their Functions.