In this paper, a new representation for the chi-squared distribution has been derived over wireless sensor networks (WSN). The underlying correlated data proliferation protocols have strong influence on performance of the deployed system. A proposed model has been deployed to investigate the WSN system over the data proliferation aspect. Initially, the degree of freedom (DOF) factor has been evaluated with respect to scalability issue in the proposal. Further, the factors affecting the outcome of the WSN system assessing data proliferation have been investigated. Moreover, sensor node operations namely: sense count, transmit count and receive redundant count have also been evaluated. Finally, extensive simulation analysis has been carried out to prove the validity of the proposed innovative scheme. However, it has also been investigated that chi-distribution for wireless sensor networks seems intractable with the degree of freedom, when varied with a specific number of nodes.