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Logistic Distribution


LogisticDistribution

The continuous distribution with parameters m and b>0 having probability and distribution functions

P(x)=(e^(-(x-m)/b))/(b[1+e^(-(x-m)/b)]^2)
(1)
D(x)=1/(1+e^(-(x-m)/b))
(2)

(correcting the sign error in von Seggern 1993, p. 250). The distribution function is similar in form to the solution to the continuous logistic equation

 x=1/(1+e^(-rt)(1/(x_0)-1)),
(3)

giving the distribution its name.

The logistic distribution is implemented in the Wolfram Language as LogisticDistribution[mu, beta].

The mean, variance, skewness, and kurtosis excess are

mu=m
(4)
sigma^2=1/3pi^2b^2
(5)
gamma_1=0
(6)
gamma_2=6/5.
(7)

See also

Logistic Equation, Lorentzian Function, Sigmoid Function

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References

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

Referenced on Wolfram|Alpha

Logistic Distribution

Cite this as:

Weisstein, Eric W. "Logistic Distribution." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LogisticDistribution.html

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