Logistic Distribution

$\begin{figure}\begin{center}\BoxedEPSF{LogisticDistribution.epsf scaled 650}\end{center}\end{figure}$

$\displaystyle P(x)$	$\textstyle =$	$\displaystyle {e^{(x-m)/b}\over \vert b\vert [1+e^{(x-m)/b}]^2}$	(1)
$\displaystyle D(x)$	$\textstyle =$	$\displaystyle {1\over 1+e^{(m-x)/\vert b\vert}},$	(2)

$\displaystyle \mu$	$\textstyle =$	$\displaystyle m$	(3)
$\displaystyle \sigma^2$	$\textstyle =$	$\displaystyle {\textstyle{1\over 3}} \pi^2\beta^2$	(4)
$\displaystyle \gamma_1$	$\textstyle =$	$\displaystyle 0$	(5)
$\displaystyle \gamma_2$	$\textstyle =$	$\displaystyle {\textstyle{6\over 5}}.$	(6)

References

von Seggern, D. CRC Standard Curves and Surfaces. Boca Raton, FL: CRC Press, p. 250, 1993.