LogisticDistribution

The logistic distribution with location $\mu$ and scale $\beta$ .

LogisticDistribution(mu, beta)an inert distribution object — carries

\mu, \beta

, unevaluated.

Typed signatures

Type	Package	Applies
`(real, real<0..>) -> distribution`	`statistics`	always

Domain: Statistics

Details

$PDF(x) = e^{-(x-\mu)/\beta} \big/ \big(\beta(1+e^{-(x-\mu)/\beta})^2\big)$ , exact.
$CDF(x) = 1/(1+e^{-(x-\mu)/\beta})$ , exact.
$Mean = \mu$ , $Variance = \beta^2\pi^2/3$ , both exact.
RandomVariate samples via inverse transform: $\mu + \beta\log(U/(1-U))$ .