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The density of the GED distribution is given by

\begin{align} GED(l;\mu,\beta,\nu)&=\frac{\nu \exp\left[-(\frac{1}{2}) \left|\frac{l-\mu}{\beta \lambda}\right|^\nu \right]} {\lambda 2^{(1+1/\nu)}\beta\Gamma (1/\nu)} \end{align} where $\Gamma(\cdot)$ is the gamma function and \begin{align*} \lambda&=\left[ 2^{(-2/\nu)}\Gamma(1/\nu) / \Gamma(3/\nu)\right]^{\frac{1}{2}} \end{align*}

how to calculate the variance?

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I found it at: Computational Finance of George Levy page appendix I.

http://tinypic.com/r/2cgif7/5

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