In this paper, we propose and clarify distributed Information Retrieval (IR) manner use of Peer-to-Peer (P2P) technology, which has the same accuracy approximately at current index-integrated search engine use of statistical information calculated from the contents. Realizing Decentralized IR systems which uses of statistic information, we need to solve following three problems. First is the calculation manner of the statistic information from all content and generating indices manner by the collaboration among distributed peers (nodes). Second problem is the efficiency of index distribution on logical space collaborated by peers named Multiple-Ring. And the last problem is efficient IR strategies with high accuracy. As for the result of the evaluation, we discuss the relationship between the propagation time for generating the statistics information and the system scalability by simulation and emulation. And our proposed system is suitable for the flexible IR service which adapts contents environment from small scale network to middle scale network such as an office.