HalfCauchy Distribution

If $Z$ is Hyperbolic Secant distributed then $e^Z$ is Half-Cauchy distributed. Also, if $W$ is (standard) Cauchy distributed, then $\left|W\right|$ is Half-Cauchy distributed. Special case of the Folded Cauchy distribution with $c=0.$ The support is $x\ge 0$. The standard form is

where $\mathrm{Si}(t)={\int }_0^t\frac{\sin x}{x}dx$, $\mathrm{Ci}(t)=-{\int }_t^{\infty }\frac{\cos x}{x}dx$.

No moments, as the integrals diverge.

Implementation: scipy.stats.halfcauchy