.. _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