Left-skewed Lévy Distribution#

Special case of Lévy-stable distribution with $\alpha=\frac{1}{2}$ and $\beta=-1$ . The support is $x\leq0$ . In standard form

\begin{array}{rcl} f (x) & = & \frac{1}{| x | \sqrt{2 π | x |}} \exp (- \frac{1}{2 | x |}) \\ F (x) & = & 2 Φ (\frac{1}{\sqrt{| x |}}) - 1 \\ G (q) & = & - {[Φ^{- 1} (\frac{q + 1}{2})]}^{- 2} . \end{array}

$\begin{eqnarray*} f\left(x\right) & = & \frac{1}{\left|x\right|\sqrt{2\pi\left|x\right|}}\exp\left(-\frac{1}{2\left|x\right|}\right)\\ F\left(x\right) & = & 2\Phi\left(\frac{1}{\sqrt{\left|x\right|}}\right)-1\\ G\left(q\right) & = & -\left[\Phi^{-1}\left(\frac{q+1}{2}\right)\right]^{-2}.\end{eqnarray*}$

No moments.

Implementation: scipy.stats.levy_l