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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)

and the Mean, Variance, Skewness, and Kurtosis are
$\displaystyle \mu$ $\textstyle =$ $\displaystyle m$ (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)

See also Logistic Equation, Logistic Growth Curve


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

© 1996-9 Eric W. Weisstein