Nonparametric estimation by iterated function systems and optimization problems: ... We study relative efficiency of the IFS estimators with respect to the e.d.f. for small samples via Monte Carlo approach. For well behaved distribution functions F and for a particular family of so-called wavelet maps the IFS estimators can be dramatically better than the e.d.f. (or the kernel estimator for density estimation) in presence of missing data, i.e., when it is only possibile to observe data on subsets of the whole support of F. This research has also produced a free package for the R statistical environment which is ready to be used in applications. (ifs: Iterated Function Systems)