Half-Cauchy distribution
= Half-Cauchy distribution
{title2=$f(x)=2\gamma/[\pi(\gamma^2+x^2)],\quad x>0$}
The absolute value of a centered <Cauchy distribution> variable with scale $\gamma>0$ has this <probability density function>. Its positive support and doubled density distinguish it from the two-sided distribution. Its unit-scale case arises as the ratio of two independent, equally scaled <half-normal distribution> variables.