I'm trying to find the MLE of $\frac{1}{\theta}$ for iid $Beta(\theta,1)$ RV's.
If I want to find the MLE of $\theta$, the normal calculation for computing the MLE gives $\hat{\theta}=-\frac{n}{\sum_{i=1}^n\log X_i}$. For finding MLE of $\frac{1}{\theta}$, should I do change of variables in the very first step of calculation? Thank you.