Peak water demand is one of the most stringent operative conditions for a Water Distribution System (WDS), not only for the intensity of the event itself, but also for its recurring nature. The estimation of the maximum water demand is a crucial aspect in both the design and management processes. Studies in the past have tackled this issue with deterministic approaches, even if peak phenomena are distinctly random. In this work, probabilistic models have been developed to study and forecast the daily maximum residential water demand. Some probability distributions have been tested by means of statistical inferences on different data samples related to three monitored WDS. The parameter estimations of the proposed equations have been related to the number of supplied users. Furthermore, this work investigates time scaling effects on the effectiveness of the proposed distributions and relations. Corrective factors that take into account the effect of time averaging step on the above-mentioned parameters have been proposed.