2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/130480We consider estimation of the structural distribution function of the cell probabilities of a multinomial sample in situations where the number of cells is large. We review the performance of the natural estimator, an estimator based on grouping the cells and a kernel type estimator. Inconsistency of the natural estimator and weak consistency of the other two estimators is derived by Poissonization and other, new, technical devices.Statistics Theory62G05; 62G20text