  In this paper we consider a class of nonparametric estimators of a
distribution function F, with compact support, based on the theory of IFSs. The
estimator of F is tought as the fixed point of a contractive operator T defined
in terms of a vector of parameters p and a family of affine maps W which can be
both depend of the sample (X_1, X_2, ...., X_n). Given W, the problem consists
in finding a vector p such that the fixed point of T is ``sufficiently near''
to F. It turns out that this is a quadratic constrained optimization problem
that we propose to solve by penalization techniques. If F has a density f, we
can also provide an estimator of f based on Fourier techniques. IFS estimators
for F are asymptotically equivalent to the empirical distribution function
(e.d.f.) estimator. We will 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.
