Driven by 6G networking, Edge Intelligence (EI) makes the most of the widespread edge resources to gain Artificial Intelligence (AI) insight. Future time-critical and data-intensive applications need distributed AI (DAI) and analytics solutions on the Edge computing platforms to enable EI from small devices to whole industrial factories. To deal with critical challenges of DAI implementation such as communication reliability, resource constrains and heterogeneity of edge devices, and dynamic nature of edge computing environment, we integrate digital twin (DT) technology to form an efficient framework. With this framework, efficient DT models are developed for edge devices, edge servers, and edge networks to predict accurately the states of physical entities using probabilistic graphical models (PGMs) and machine learning (ML) algorithms. In addition, a DT-empowered edge computing architecture specifying the optimal edge server placement, DT placement, and edge clustering is developed to support the implementation and development of DAI solutions. Specially, the framework is able to support various task partitioning-based DAI models including data parallelism, model parallelism, and pipeline parallelism as well as federated learning.