Estimation of the parameters of a compactly-supported model stable under the violation of compact supportedness

We consider two approaches to the problem of robust estimations of the distribution parameters of a random variable whose range is bounded (from either or both sides). The traditional approach gives stable parameter estimates only when the actual and model random variables have the same range. The generalized approach introduced in the paper can be applied in the presence of observations lying outside the range of the model random variable. It is shown that, under some conditions, these approaches are asymptotically equivalent.