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.. _continuous-levy:
Lévy Distribution
==================
A special case of Lévy-stable distributions with :math:`\alpha=\frac{1}{2}`
and :math:`\beta=1` and support :math:`x\geq0`. In standard form it is defined for :math:`x>0` as
.. math::
:nowrap:
\begin{eqnarray*} f\left(x\right) & = & \frac{1}{x\sqrt{2\pi x}}\exp\left(-\frac{1}{2x}\right)\\ F\left(x\right) & = & 2\left[1-\Phi\left(\frac{1}{\sqrt{x}}\right)\right]\\ G\left(q\right) & = & \left[\Phi^{-1}\left(1-\frac{q}{2}\right)\right]^{-2}.\end{eqnarray*}
It has no finite moments.
Implementation: `scipy.stats.levy`
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