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Distribution System State Estimation (DSSE) is nowadays essential to enable the smart management of medium and low voltage grids. Due to the lack of a suitable measurement infrastructure, DSSE usually relies on the use of power injection pseudo-measurements derived from the knowledge of the historical and statistical behaviour of loads and generators. The uncertainty of these pseudo-measurements could not fit with the normal distribution typically considered in DSSE. For this reason, suitable approaches have to be designed both to model the pseudo-measurements uncertainty and to consider it in the DSSE process. This paper proposes a DSSE algorithm based on the Bayesian theory able to handle appropriately pseudo-measurements with any uncertainty distribution. The procedure used to cluster different categories of prosumers and to generate the pseudo-measurement parameters provided as input …