We propose and clarify the manner in which a distributed information retrieval (IR) is conducted using a Peer-to-Peer (P2P) technology that has approximately the same accuracy as a current index-integrated search engine with the statistical information calculated from the contents. We need to solve the following three problems to develop distributed IR services that use statistic information. The first one is the manner of the calculation of the statistic information from all the contents and then generating the manner of the indices using the collaboration among distributed peers (nodes). The second problem is the efficiency of the index distribution on the logical space collaborated by the peers which is named the Multiple-Ring. The last problem is having efficient IR strategies that are highly accurate. We discuss the relationship between the propagation time for generating the statistics information and the system scalability by using simulations and emulations to evaluate the results. Our proposed system is suitable for flexible IR services that use the content environment of small to mid-scale networks such as those in an office.