The penetration of wind power is increasing in distribution network for reducing reliance on fossil fuels and covering continuously increasing demand for energy. However, it is argued that the forecasting error of wind power cannot be avoided even using the best forecasting approach. Therefore, in this study, a mean-variance-skewness based expectation maximisation (MVSbEM) model has been proposed by maximisation of the mean and skewness while simultaneously minimisation of the variance to obtain the optimal trade-off relationship between the profit and risk of distribution network planning (DNP) considering uncertain wind power integrated. In the MVSbEM model, the indexes of network loss, voltage deviation, and investment cost are concurrently taken into account under several kinds of actual operation constraints. In addition, the authors have made a full investigation on the MVSbEM by considering different forecasting errors, power factors of wind power, the different forecasting wind speeds, the number of wind turbines as well as the lines and substations upgrading. Furthermore, in order to reduce the computational burden, the Latin hypercube sampling method is used to sample uncertain wind speed. The feasibility and effectiveness of the MVSbEM model have been comprehensively evaluated on a modified IEEE 33-bus system.