Kappa 4 parameter distribution

The probability density function for the Kappa 4 parameter distribution is:

if :math:h != 0, k != 0:

.. math::

f(x, h, k) = (1 - k x)^{1/k - 1} (1 - h (1 - k x)^{1/k})^{1/h-1}

if :math:h == 0, k != 0:

.. math::

f(x, h, k) = (1.0 - k*x)**(1.0/k - 1.0) * exp(-(1.0 - k*x)**(1.0/k))

if :math:h != 0, k == 0:

.. math::

f(x, h, k) = exp(-x)*(1.0 - h*exp(-x))**(1.0/h - 1.0)

if :math:h == 0, k == 0:

.. math::

f(x, h, k) = exp(-x)*exp(-exp(-x))

The following plots show the pdf and cdf:

.. image:: ../../../../tests/imgs/stats/continuous/kappa4/kappa4pdf.png :align: center :width: 480

.. image:: ../../../../tests/imgs/stats/continuous/kappa4/kappa4cdf.png :align: center :width: 480