Exponential power distribution

The probability density function for the exponential power distribution is

.. math::

f(x,b) = bx^{b-1}\exp(1+x^b-\exp(x^b))

for :math:x\ge 0, b>0. Here :math:b is a shape parameter.

The cumulative distribution function is

.. math::

F(x,b) = 1-\exp(1-\exp(x^b))

The following plots show the pdf and cdf:

.. image:: ../../../../tests/imgs/stats/continuous/exponpow/exponpowpdf.png :align: center :width: 480

.. image:: ../../../../tests/imgs/stats/continuous/exponpow/exponpowcdf.png :align: center :width: 480