# Definition:Logistic Distribution

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## Definition

Let $X$ be a continuous random variable on a probability space $\struct {\Omega, \Sigma, \Pr}$.

Let $\Img X = \R$.

$X$ is said to have the logistic distribution if and only if it has probability density function:

$\map {f_X} X = \dfrac {\map \exp {-\dfrac {\paren {x - \mu} } s} } {s \paren {1 + \map \exp {-\dfrac {\paren {x - \mu} } s} }^2}$

for $\mu \in \R, s \in \R_{>0}$.

This is written:

$X \sim \map {\operatorname {Logistic} } {\mu, {s} }$

## Also see

• Results about the logistic distribution can be found here.