The continuous distribution with parameters 
and 
having probability
and distribution functions
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(1)
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(2)
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(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
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(3)
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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
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(4)
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(5)
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(6)
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(7)
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