# 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

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