For sample size large enough, we know that the Maximum likelihood estimator (MLE) is asymptotic efficient. So when we have two classical methods (MLE and method of moment estimators) for inference of Normal distribution (or Uniform distribution on $[0,\theta]$ with unknown $\theta$), we prefer to use the MLE but not method of moment estimators.
But there is still some advantages of MoM estimators, like it is easy to compute. Can we find some examples for inference distribution that MoM would be better than MLE?
