Gilbrat distribution

The probability density function for the gilbrat distribution is:

.. math::

f(x) = \frac{1}{x \sqrt{2\pi}} \exp(-\frac{1}{2} (\log(x))^2)

The cumulative distribution function is:

.. math::

F(x) = {\rm NormCDF}(\log(x))

where NormCDF is the cumulative density function of the standard normal distribution. The following plots show the pdf and cdf:

.. image:: ../../../../tests/imgs/stats/continuous/gilbrat/gilbratpdf.png :align: center :width: 480

.. image:: ../../../../tests/imgs/stats/continuous/gilbrat/gilbratcdf.png :align: center :width: 480