In this paper, we consider the minimum Cramer-von Mises distance estimator for parametric families of distributions and we derive its asymptotic properties. We treat the situation where complete data are available as well as the one where data are grouped into intervals. The influence function for the estimator is derived and used to show that the estimator is asymptotically normal. We are able to compute the estimator's approximate variance for a few selected models, but more generally, we show how to consistently estimate both the influence function and the variance estimator. Moreover, we see that in many cases, the influence function of the estimator is bounded, a robustness property which is desirable in the context of estimation of insurance loss distribution.