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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