Let P be a probability measure on the real line with Lebesque-density f. The usual estimator of the distribution function (≡df) of P for the sample $chi$$_1$,…, $chi$$\_$n/ is the empirical df: F$\_$n/(t)=(equation omitted). But this estimator does not take into account the smoothness of F, that is, the existence of a density f. Therefore, one should expect that an estimator which is better adapted to this situation beats the empirical df with respect to a reasonable measure of performance.(omitted)