Statistical service has been proposed for service differentiation networks to improve resource utilization. However, it has remained in a challenge to compute end-to-end statistical service bounds for aggregates of regulated flows in a network. In this paper, we develop a generalized statistical traffic envelope, global statistical envelope, which covers not only aggregated traffic of regulated flows, but also a large variety of traffic sources. Based on this characterization, we derive statistical bounds on delay and backlog in a service curve network. The general results are further applied to computing statistical delay bound of aggregated flows regulated by peak rate constrained leaky buckets in a network of rate-latency servers. The effectiveness of our theoretical results as verified by numerical evaluation in terms of providing significantly tight delay bounds.