Argus distribution

The probability density function for Argus distribution is:

.. math::

f(x,\chi) = \frac{\chi^3}{\sqrt{2\pi}\Psi(\chi)}x\sqrt{1-x^2}\exp(-\chi^2(1-x^2)/2)

for :math:0<x<1 and :math:\chi>0, where

.. math::

\Psi(\chi) = \Phi(\chi) - \chi\phi(\chi) - \frac{1}{2}

where :math:\Phi and :math:\phi are the CDF and PDF of the normal distribution, respectively.

The cumulative density function is:

.. math::

F(x,\chi) = 1 - \frac{\Psi(\chi\sqrt{1-x^2})}{\Psi(\chi)}

The following plots show the pdf and cdf:

.. image:: ../../../../tests/imgs/stats/continuous/argus/arguspdf.png :align: center :width: 480

.. image:: ../../../../tests/imgs/stats/continuous/argus/arguscdf.png :align: center :width: 480