左偏莱维分布#

莱维稳定分布的特殊情况，其中 \(\alpha=\frac{1}{2}\) 且 \(\beta=-1\)。其支撑集为 \(x\leq0\)。标准形式为

\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*}