I currently have a probability density with 2 parameter $\alpha $ and $\beta$. I've calculated $\hat{\alpha},\hat{\beta}$ aswell as the expected information $I_G$.
If I now want the MLE of $\gamma$ where $\gamma=\frac{\alpha}{\beta}$, would the in-variance property of MLE let me make the statement that $\hat{\gamma}=\frac{\hat{\alpha}}{\hat{\beta}}$
What would the asymptotic distribution of $\hat\gamma$ be? If It is an MLE it will be asymptotically normal with mean $\gamma_0$ but what sort of transformation could I apply to get the variance of $\hat\gamma$