Given a sample of size n, a continuous estimator for a distribution F (based on Pyke's modified sample distribution) is shown to have the property that its expected squared error, for almost all x in the positive sample space of F, is no larger than that of the sample distribution function given F and n sufficiently large. Letting risk be given by the expected squared error integrated with respect to F, it is shown that this estimator dominates both the sample distribution and the other best invariant estimator found by Aggarwal, given F and n sufficiently large. Other common estimators cannot serve in this dominating role. Explicit calculation of risk is made when F is the uniform distribution. In this case the estimator strictly dominates the sample distribution for all n \geqq 1.