To address the severe challenges posed by extreme weather events such as typhoons to the safe and stable operation of power systems, a distributed robust unit commitment model considering multivariate random variables is proposed in this paper. First, the output model of new energy units and the fault probability model of power grid equipment under typhoon disasters are constructed. Then, a three-layer min-max-min distributed robust optimal scheduling model under typhoon disasters is established. Based on this, considering the influence of multivariate random variables, a fuzzy set of fault probability distributions is developed, incorporating both the worst-case failures and the most probable failures. Finally, the model is solved using the column-and-constraint generation algorithm, and case studies are conducted on the improved IEEE118-bus system. Results show that, compared with traditional robust optimization models, the proposed method achieves a better balance between robustness and economic performance of the power system.