This paper presents a novel rapid estimation method (REM) to perform stochastic impact analysis of grid-edge technologies (GETs) to the power distribution networks. The evolution of network states' probability density functions (PDFs) in terms of GET penetration levels are characterized by the Fokker-Planck equation (FPE). The FPE is numerically solved to compute the PDFs of network states, and a calibration process is also proposed such that the accuracy of the REM is maintained for large-scale distribution networks. The approach is illustrated on a large-scale realistic distribution network using a modified version of the IEEE 8500 feeder, where electric vehicles (EVs) or photovoltaic systems (PVs) are installed at various penetration rates. It is demonstrated from quantitative analyses that the results from our proposed approach have negligible errors comparing with those obtained from Monte Carlo simulations.