Real-time and embedded systems are shifting from single-core to multi-core processors, on which software must be parallelized to fully utilize the computation capacity of hardware. Recently much work has been done on real-time scheduling of parallel tasks modeled as directed acyclic graphs (DAG). However, most of these studies assume tasks to have implicit or constrained deadlines. Much less work considered the general case of arbitrary deadlines (i.e., the relative deadline is allowed to be larger than the period), which is more difficult to analyze due to intra-task interference among jobs. In this paper, we study the analysis of Global Earliest Deadline First (GEDF) scheduling for DAG parallel tasks with arbitrary deadlines. We develop new analysis techniques for GEDF scheduling of a single DAG task, which not only outperform the state-of-the-art in general evidenced by empirical evaluation, but also guarantee a better capacity augmentation bound 2.41 (the best known result is 2.5). The proposed analysis techniques are also extended to and evaluated with the case of multiple DAG tasks using the federated scheduling approach.