In this paper we consider the estimation of the distribution function when data come from a non-probability sample. We refer to non-probability sample as one in which the sampling mechanism generating our data is not known a priori. In this context, it is not possible to directly apply the classical design-based approach to make inference about the finite population parameters. The arbitrary selection of units into the sample implies that the non-probability sample fails to properly represent the target population. This issue motivated us to introduce measures to quantify the uncertainty of the parameter estimates.