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The electrical load pattern representing the residential consumption is subject to different types of uncertainty, depending on family composition, lifestyle, number and type of use of the electrical appliances, thus requiring a dedicated analysis within a probabilistic framework. A comprehensive approach to the probabilistic characterisation of aggregated residential consumers supplied by the same feeder or substation, from the point of view of the electricity supplier, is presented. Starting from the result of a statistical study carried out on single-house extra-urban residential consumers, the time evolution of the average value and the standard deviation of the aggregated load power are presented. In addition, a dedicated goodness-of-fit analysis has been carried out to identify the most suitable probability distributions representing the daily aggregated load pattern at different times, referred to a set of typical days. This analysis includes a novel characterisation of the critical error of the Kolmogorov-Smirnov test on various probability distributions (beta, gamma, Gumbel, log-normal, Rayleigh and Weibull) for which the critical errors are not specifically available in publications. The gamma and log-normal probability distributions have emerged as the most promising solutions for several time intervals of analysis and for different numbers of aggregated consumers.