In this paper, we introduce a nonparametric end-to-end method for probabilistic forecasting of distributed renewable generation outputs while including missing data imputation. Firstly, we employ a nonparametric probabilistic forecast model utilizing the long short-term memory (LSTM) network to model the probability distributions of distributed renewable generations' outputs. Secondly, we design an end-to-end training process that includes missing data imputation through iterative imputation and iterative loss-based training procedures. This two-step modeling approach effectively combines the strengths of the nonparametric method with the end-to-end approach. Consequently, our approach demonstrates exceptional capabilities in probabilistic forecasting for the outputs of distributed renewable generations while effectively handling missing values. Simulation results confirm the superior performance of our approach compared to existing alternatives.