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Half-Logistic Distribution

docs/tutorial:stats:continuous_halflogistic

In the limit as $c \to \infty$ for the generalized half-logistic we have the half-logistic defined over $x \geq 0.$ Also, the distribution of $∣ X ∣$ where $X$ has logistic distribution.

M (t) = 1 - t ψ_{0} (\frac{1}{2} - \frac{t}{2}) + t ψ_{0} (1 - \frac{t}{2})

where $ψ_{m}$ is the polygamma function $ψ_{m} (z) = \frac{d ^{m + 1}}{d z ^{m + 1}} lo g (Γ (z))$ .

μ_{n}^{'} = 2 (1 - 2^{1 - n}) n! ζ (n) n \neq = 1

Implementation: scipy.stats.halflogistic