Journal of Applied Mathematics and Decision Sciences
Volume 2005 (2005), Issue 1, Pages 33-46

Approximating distribution functions by iterated function systems

Stefano Maria Iacus and Davide La Torre

Department of Mathematics, University of Ulster, Ireland

Received 1 August 2003; Revised 24 January 2004

Copyright © 2005 Stefano Maria Iacus and Davide La Torre. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An iterated function system (IFS) on the space of distribution functions is built with the aim of proposing a new class of distribution function estimators. One IFS estimator and its asymptotic properties are studied in detail. We also propose a density estimator derived from the IFS distribution function estimator by using Fourier analysis. Relative efficiencies of both estimators, for small and moderate sample sizes, are presented via Monte Carlo analysis.