Definition:Logistic Distribution
Jump to navigation
Jump to search
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.
Sources
- Weisstein, Eric W. "Logistic Distribution." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LogisticDistribution.html