Trends in Applied Sciences Research1819-35792151-7908Science International10.3923/tasr.2019.1.6TarrayTanveer Ahmad SinghHousila Prasad MasoodSaadia 12019141Background and Objective: The crux of this paper is to develop a new a distinct question randomized response model for estimating a rare sensitive attribute using Poisson distribution. Methodology: The equilibrium point of the model was investigated and a new stratified sampling and stratified sampling randomized response model is proposed. Results: It has suggested an unbiased estimator of the mean number of persons possessing the rare sensitive attribute in presence of the unknown proportion of persons possessing a rare unrelated attribute. The addressed issue is resolved by using Lagrange multipliers technique and the optimum allocation is acquired in the form of fuzzy numbers. Conclusion: Anew dexterous stratified randomized response model has been proposed and properties of the proposed randomized response model have been studied. Numerical it has shown that the suggested randomized response model is superior one.]]>Warner, S.L.,1965606369Horvitz, D.G., B.V. Shah and W.R. Simmons,19671967pp: 6572Greenberg, B.G., A.L.A. Abul-Ela, W.R. Simmons and D.G. Horvitz,196964520539Singh, H.P. and N. Mathur,200446375378Singh, H.P. and N. Mathur,2005131135144Singh, S., S. Horn, R. Singh and N.S. Mangat,20036515522Kim, J.M. and W.D. Warde,2004120155165Kim, J.M. and M.E. Elam,20056117Kim, J.M. and M.E. Elam,200748215233Singh, H.P. and T.A. Tarray,201219751759Singh, H.P. and T.A. Tarray,20133459472Land, M., S. Singh and S.A. Sedory,201246351360Lee, G.S., D. Uhm and J.M. Kim,201347575589Singh, H.P. and T.A. Tarray,2014904245Singh, S., R. Singh, N.S. Mangat and D.S. Tracy,199454233243