For iid random variables from a distribution with p.d.f.
$f(x;\theta_1,\theta_2)=\frac{1}{\theta_2}\exp\bigg(-\frac{(x-\theta_1)}{\theta_2}\bigg), \quad x>\theta_1, \quad(\theta_1,\theta_2)\in\mathbb{R}\times\mathbb{R}^{+}$ how can we find maximum likelihood estimators for $\theta_1$ and $\theta_2$?
I don't think finding the log-likelihood and performing partial deffierentiation will help for determining the MLE of $\theta_1$ because of the $x>\theta_1$ condition.
Any help would be greatly appreciated. Regards, MM.