Folded Cauchy Distribution#

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. There is one shape parameter \(c\) and the support is \(x\geq0.\)

\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(q;c\right)\end{eqnarray*}

No moments

Implementation: scipy.stats.foldcauchy