The goal of moving object segmentation is separating moving objects from stationary backgrounds in videos. One major challenge in this problem is how to develop a universal model for videos from various natural scenes since previous methods are often effective only in specific scenes. In this paper, we propose a method called Learning Temporal Distribution and Spatial Correlation (LTS) that has the potential to be a general solution for universal moving object segmentation. In the proposed approach, the distribution from temporal pixels is first learned by our Defect Iterative Distribution Learning (DIDL) network for a scene-independent segmentation. Notably, the DIDL network incorporates the use of an improved product distribution layer that we have newly derived. Then, the Stochastic Bayesian Refinement (SBR) Network, which learns the spatial correlation, is proposed to improve the binary mask generated by the DIDL network. Benefiting from the scene independence of the temporal distribution and the accuracy improvement resulting from the spatial correlation, the proposed approach performs well for almost all videos from diverse and complex natural scenes with fixed parameters. Comprehensive experiments on standard datasets including LASIESTA, CDNet2014, BMC, SBMI2015 and 128 real world videos demonstrate the superiority of proposed approach compared to state-of-the-art methods with or without the use of deep learning networks. To the best of our knowledge, this work has high potential to be a general solution for moving object segmentation in real world environments. The code and real-world videos can be found on GitHub https://github.com/guanfangdong/LTS-UniverisalMOS.