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Replication strategy has been considered as a promising technique for improving data accessibility as well as reducing gateway overload in wireless mesh networks (WMNs). In this regard, popular data is stored in some indicated mesh routers within the network being closer to the users. However, in video streaming applications over WMNs, due to the large size of the videos, it is very challenging for replication strategies to achieve a high quality of experience (QoE) while consuming a minimum storage capacity requirement (SCR). In this paper, as a solution, we propose a novel replication strategy to overcome such challenge by determining an optimal replication density for each segment of a video streaming. The optimal result is based on exploiting not only the skewed access probabilities of video segments as conventional replication strategies but also the skewed encoding rate-distortion information and the loss probability of each frame of a segment. We carefully study the optimization problem in two forms. In the original problem form, our method consumes a minimum SCR under a given constraint of quality playback. In the duality problem form, the proposed scheme provides highest quality playback for a given SCR constraint. Simulation results show that our proposed approach gains a better performance in terms of QoE improvement and SCR saving compared to other existing replication strategies.