2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/130458In this paper an iterated function system on the space of distribution functions is built. The inverse problem is introduced and studied by convex optimization problems. Some applications of this method to approximation of distribution functions and to estimation theory are given.1 tableStatistics Theory62E17; 62H10; 37Htext