Generalized Logistic Distribution

Has been used in the analysis of extreme values. There is one shape parameter $c>0$. The support is $x\in \mathcal{R}$.

Note that the polygamma function is

where $\zeta \left(k,x\right)$ is a generalization of the Riemann zeta function called the Hurwitz zeta function. Note that $\zeta \left(n\right)\equiv \zeta \left(n,1\right)$.

Implementation: scipy.stats.genlogistic