Consider the formulas developed for the Gamma distribution 8.4.8 with that \(\mu=2\) amd \(r\) replaced with \(r/2\text{.}\) This gives
\begin{equation*} \mu = \frac{r}{2}2 = r \end{equation*}
\begin{equation*} \sigma^2 = \frac{r}{2}2^2 = 2r \end{equation*}
\begin{equation*} \gamma_1 = \frac{2}{\sqrt{\frac{r}{2}}} = \frac{2^{3/2}}{\sqrt{r}} \end{equation*}
\begin{equation*} \gamma_2 = \frac{6}{\frac{r}{2}} + 3 = \frac{12}{r} + 3 \end{equation*}