# Logistic law

In Probability, the logistic law of parameter μ and S > 0 is a Loi of probability whose density is

$f \left(X\right) = \ frac \left\{e^ \left\{- \ frac \left\{X \ driven\right\} \left\{S\right\}\right\}\right\} \left\{S \ left \left(1+e^ \left\{- \ frac \left\{X \ driven\right\} \left\{S\right\}\right\} \ right\right) ^2\right\}$
Its function of distribution is
$F \left(X\right) = \ frac \left\{1\right\} \left\{1+e^ \left\{- \ frac \left\{X \ driven\right\} \left\{S\right\}\right\}\right\}$
Its name of logistic law is resulting owing to the fact that its density of probability is a logistic function Its hope and its variance are given by the following formulas:
$E \left(X\right) = \ driven \,$
$V \left(X\right) = \ frac \left\{s^2 \ pi^2\right\} \left\{3\right\}$
It is used in logistic Régression

The logistic law standard is the logistic law of parameter 0 and 1.

Its Fonction of distribution is the sigmoid

$F \left(X\right) = \ frac \left\{1\right\} \left\{1+e^ \left\{- X\right\}\right\}$
Its hope and its variance are given by the following formulas:
$E \left(X\right) = 0 \,$
$V \left(X\right) = \ frac \left\{\ pi^2\right\} \left\{3\right\}$

## See too

 Random links: Saint-Gervais-the-Three-bell-towers | Forest-on-Separates | George Wythe | University of management of the companies | Michael Mason | Paquet_mince_de_petit-contour