Cauchy distribution

A Cauchy continuous random variable.

Notes

The probability density function for cauchy is:

.. math::

f(x, \alpha, \beta) = \frac{\beta}{\pi [\beta^2 + (x-\alpha)^2]}\quad\beta > 0

for a real number :math:x.

The cumulative distribution function for cauchy is:

.. math::

F(x, \alpha, \beta) = \frac{1}{2} + \frac{1}{\pi}\arctan(x-\alpha/\beta)

The following plots show the pdf and cdf.

.. image:: ../../../../tests/imgs/stats/continuous/cauchy/cauchypdf.png :align: center :width: 480

.. image:: ../../../../tests/imgs/stats/continuous/cauchy/cauchycdf.png :align: center :width: 480