2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/217572In this paper we consider a random variable $Y$ contamined by an independent additive noise $Z$. We assume that $Z$ has known distribution. Our purpose is to test the distribution of the unobserved random variable $Y$. We propose a data driven statistic based on a development of the density of $Y+Z$, which is valid in the discrete case and in the continuous case. The test is illustrated in both cases.Submitted to the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org)Statistics Theory62G10 (Primary) 62F05 (Secondary)text