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Accurate solar photovoltaic (PV) generation forecast is critical to the reliable and economic operation of a modern power system. In practice, due to various faulty issues in the sensor, communication, or database system, the historical and online measurement data may not be always complete, and the missing data could dramatically degrade the forecasting model's accuracy. To solve this problem, this paper proposes an integrated missing-data tolerant model for probabilistic PV power generation forecasting. Taking historical PV generations as input, this model is based on a recursive long short-term memory network (Rec-LSTM), which can provide multi-step ahead forecasting of the probability distribution of PV generation. The unobserved input data will be imputed recursively based on the model output at the previous time step. During the training process, the imputations and forecasting values are iteratively updated by the negative log-likelihood loss function. As a salient advantage, this method can deal with data missing scenarios at both offline and online stages. Numerical experiments are conducted on two one-year datasets from Australia and Singapore, respectively. Probabilistic forecasting for both large-scale and small-scale building-level PV power generation is tested at the time resolution of 15 mins. Testing results show the proposed method can achieve superior probabilistic prediction accuracy as well as strong robustness under various data missing scenarios, compared to other state-of-the-art methods. [ABSTRACT FROM AUTHOR]