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SciPy

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Logistic (Sech-squared) Distribution

A special case of the Generalized Logistic distribution with c=1. Defined for x>0

f(x)=exp(x)[1+exp(x)]2F(x)=11+exp(x)G(q)=log(1/q1)
μ=γ+ψ0(1)=0μ2=π26+ψ1(1)=π23γ1=ψ2(c)+2ζ(3)μ3/22=0γ2=(π415+ψ3(c))μ22=65md=log1=0mn=log(21)=0
h[X]=1.

Implementation: scipy.stats.logistic