Journal of Applied Mathematics and Decision Sciences 
Volume 2005 (2005), Issue 1, Pages 33-46
doi:10.1155/JAMDS.2005.33

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

Abstract

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.