Generalized logistic distribution

The probability density function for the generalized logistic distribution is:

.. math::

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

where :math:x \ge 0, c > 0.

The cumulative distribution function is:

.. math::

F(x, c) = (1 + e^{-x})^{-c}

The following plots show the pdf and cdf:

.. image:: ../../../../tests/imgs/stats/continuous/genlogistic/genlogisticpdf.png :align: center :width: 480

.. image:: ../../../../tests/imgs/stats/continuous/genlogistic/genlogisticcdf.png :align: center :width: 480