nature of the spread parameter in the Levy distribution

Question

The reflected Levy distribution is given by $$ p(x):= \left\{ \begin{array}{lcl} \sqrt{\frac{\sigma}{2\pi}}e^{-\frac{\sigma}{2(\mu-x)}}\cdot (\mu-x)^{-\frac{3}{2}} &,& \text{if}\; x\leq\mu\\ 0 &,& \text{if}\; x>\mu \end{array} \right. $$ where $\mu>0$ and $\sigma>0$ are the location and the spread parameters, respectively. Is the spread parameter, $\sigma$, identical to the standard deviation of this distribution? If it is not, what is the standard deviation of $p$?