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The rapid growth in use of renewable intermittent energy resources, like wind turbines (WTs) and solar panels, in distribution networks has increased the need for having an accurate and efficient method of handling the uncertainties associated with these technologies. In this paper, the unsymmetrical two point estimate method (US2PEM) is used to handle the uncertainties of renewable energy resources. The uncertainty of intermittent generation of WT, photo voltaic cells, and also electric loads, as input variables, are taken into account. The variation of active losses and imported power from the main grid are defined as output variables. The US2PEM is compared to symmetrical two point estimate method, Gram-Charlier method, and Latin hypercube sampling method, where Monte Carlo simulation is used as a basis for comparison. The validity of the proposed method is examined by applying it on a standard radial 9-node distribution network and a realistic 574-node distribution network.