Distributed Antenna Systems (DAS) play a key role in future wireless communications. Despite the increasing previous research work, the channel models of DAS lack generality. This paper presents a holistic and generic channel model, which incorporates path loss, lognormal shadowing, and generalized-gamma fast fading into consideration. This overarching composite channel model encompasses well-known composite channel models as special cases. A probabilistic system outage model is attained by selective transmission scheme in terms of the proposed channel model and the distribution of mobile stations in the cell. Experimental results substantiate that the theoretical model provides sufficient precision for evaluating the outage performance of DAS.