Half-Cauchy distribution

The probability density function for the Half-Cauchy distribution is:

.. math::

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

where :math:x \ge 0. The cumulative distribution function is:

.. math::

F(x) = \frac{\pi}{2} arctan(x)

The following plots show the pdf and cdf:

.. image:: ../../../../tests/imgs/stats/continuous/halfcauchy/halfcauchypdf.png :align: center :width: 480

.. image:: ../../../../tests/imgs/stats/continuous/halfcauchy/halfcauchycdf.png :align: center :width: 480