Folded Cauchy DistributionΒΆ
This formula can be expressed in terms of the standard formulas for the Cauchy distribution (call the cdf \(C\left(x\right)\) and the pdf \(d\left(x\right)\) ). if \(Y\) is cauchy then \(\left|Y\right|\) is folded cauchy. Note that \(x\geq0.\)
\[ \begin{eqnarray*} f\left(x;c\right) & = & \frac{1}{\pi\left(1+\left(x-c\right)^{2}\right)}+\frac{1}{\pi\left(1+\left(x+c\right)^{2}\right)}\\ F\left(x;c\right) & = & \frac{1}{\pi}\tan^{-1}\left(x-c\right)+\frac{1}{\pi}\tan^{-1}\left(x+c\right)\\ G\left(q;c\right) & = & F^{-1}\left(x;c\right)\end{eqnarray*}\]
No moments
Implementation: scipy.stats.foldcauchy