This paper introduces the terms aleatory and epistemic uncertainties for use in a stochastic hosting capacity method. The role these uncertainties play in the hosting capacity determination is illustrated. It is shown that distinction between aleatory (statistical) and epistemic (systematic) uncertainties is helpful to characterize the probability distributions correctly. For epistemic uncertainties, it is often challenging to obtain information on the probability distribution function. For aleatory uncertainties, a method for characterizing the probability distribution is presented. Aleatory uncertainties’ data measurements are used to obtain a distribution best-fit. The background voltage measurement for a customer in a low-voltage distribution network is used to illustrate the method. Values were obtained for the distribution functions of the three-phase voltages. The used distribution functions are found to influence the resulting hosting capacity. This entails that there is need for measurements and data collection. A research challenge remaining concerns the stochastic model of epistemic uncertainty.