Logistic Distribution
LogisticDistribution
The continuous distribution with parameters m and b>0 having probability and distribution functions
P(x) = [画像:(e^(-(x-m)/b))/(b[1+e^(-(x-m)/b)]^2)]
![画像:(e^(-(x-m)/b))/(b[1+e^(-(x-m)/b)]^2)](/index.cgi/contrast/https://mathworld.wolfram.com/images/equations/LogisticDistribution/Inline5.svg){kind=link}
(1)
D(x) = [画像: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
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 =
(6)
gamma_2 = 6/5.
(7)
See also
Logistic Equation, Lorentzian Function, Sigmoid FunctionExplore with Wolfram|Alpha
WolframAlpha
More things to try:
References
von Seggern, D. CRC Standard Curves and Surfaces. Boca Raton, FL: CRC Press, p. 250, 1993.Referenced on Wolfram|Alpha
Logistic DistributionCite this as:
Weisstein, Eric W. "Logistic Distribution." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LogisticDistribution.html