2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/130467By the method of Poissonization we confirm some existing results concerning consistent estimation of the structural distribution function in the situation of a large number of rare events. Inconsistency of the so called natural estimator is proved. The method of grouping in cells of equal size is investigated and its consistency derived. A bound on the mean squared error is derived.Statistics Theory62G05; 62G20text