\begin{definition}[Definition:Logistic Distribution]
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''' {{iff}} 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: 
$X \sim \map {\operatorname {Logistic} } {\mu, {s} }$
\end{definition}