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