Folded Cauchy distribution

The probability density function for the folded Cauchy distribution is:

.. math::

f(x, c) = \frac{1}{\pi (1+(x-c)^2)} + \frac{1}{\pi (1+(x+c)^2)}

where :math:x \ge 0.

The cumulative distribution function is:

.. math::

F(x, c) = \frac{1}{\pi}(\arctan(x-c) + \arctan(x+c))

The following plots show the pdf and cdf:

.. image:: ../../../../tests/imgs/stats/continuous/foldcauchy/foldcauchypdf.png :align: center :width: 480

.. image:: ../../../../tests/imgs/stats/continuous/foldcauchy/foldcauchycdf.png :align: center :width: 480