.. _continuous-foldcauchy:

Folded Cauchy Distribution

This formula can be expressed in terms of the standard formulas for the Cauchy distribution (call the cdf :math:C\left(x\right) and the pdf :math:d\left(x\right) ). If :math:Y is cauchy then :math:\left|Y\right| is folded cauchy. There is one shape parameter :math:c and the support is :math:x\geq0.

.. math:: :nowrap:

\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