Power log-normal distribution

The probability density function for power log-normal distribution is:

.. math::

f(x, a, b) = \frac{a}{x b} \phi(\log(x)/b)(\Phi(-\log(x)/b))^{a-1}

where :math:\phi is the normal pdf, and :math:\Phi is the normal cdf, and :math:x > 0, :math:a, b > 0.

The following plots show the pdf and cdf:

.. image:: ../../../../tests/imgs/stats/continuous/powerlognorm/powerlognormpdf.png :align: center :width: 480

.. image:: ../../../../tests/imgs/stats/continuous/powerlognorm/powerlognormcdf.png :align: center :width: 480