Let’s assume I have a set of samples of a random variable

$$

X = Y + Z >,

$$

where $Y$ is Gaussian (with a mean of zero and variance $sigma^2$) and $Z$ has a symmetric $alpha$-stable distribution with index of stability $alpha$ and scale parameter $c$. I know $alpha$, but I don’t know $sigma$ and $c$. How do I go about estimating them?