Pearson type III distribution

The probability density function for pearson3 distribution is:

.. math::

f(x, k) = \frac{|\beta|}{\Gamma(\alpha)}
                   (\beta (x - \zeta))^{\alpha - 1}
                   \exp(-\beta (x - \zeta))

where:

.. math::

\beta = \frac{2}{k},
\alpha = \beta^2 = \frac{4}{k^2},
\zeta = -\frac{\alpha}{\beta} = -\beta

:math:\Gamma is the gamma function.

The following plots show the pdf:

.. image:: ../../../../tests/imgs/stats/continuous/pearson3/pearson3pdf.png :align: center :width: 480