the intermittency and variability of these permeated Distributed Generators (DGs) could critically cause many security and economy risks to distribution systems. This paper applied a certain mathematical distribution to imitate the output variability and uncertainty of DGs. And then, four risk indices EENS, PLC, EFLC and SI were established to reflect the system risk level of distribution system. For the certain mathematical distribution of the DGs' output power, a developed PEM (point estimate method)-based method was proposed to calculate these four system risk indices. In this developed PEM-based method, enumeration method was used to list the states of distribution systems, an improved PEM was presented to deal with the uncertainties of DGs and the value of load curtailment in distribution systems was calculated by an optimal power flow algorithm. Finally, the effectiveness and advantages of this proposed PEM-based method for distribution system assessment were verified by the tests of a modified IEEE 30-bus system. Simulation results have shown that this proposed PEM-based method has a high computational accuracy and highly reduced computational costs compared with other risk assessment methods and is very effective for risk assessments.