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Logistic Function

Statistical properties

mean | μ
mode | β log(e^((2 μ)/β)) - μ
standard deviation | (π β)/sqrt(3)
variance | (π^2 β^2)/3
skewness | 0

Probability density function (PDF)

e^(-(x - μ)/β)/(β (e^(-(x - μ)/β) + 1)^2)

Plots of PDF for typical parameters

Plots of PDF for typical parameters

Cumulative distribution function (CDF)

P (X<=x) = 1/(e^(-(x - μ)/β) + 1)

Plots of CDF for typical parameters

Plots of CDF for typical parameters

Percentiles

10th | μ - 2.19722 β
25th | μ - 1.09861 β
50th | μ
75th | 1.09861 β + μ
90th | 2.19722 β + μ

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