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

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