A two-stage Land et al.'s randomized response model for estimating a rare sensitive attribute using Poisson distribution

The crux of this paper is to estimate the mean of the number of persons possessing a rare sensitive attribute based on the Mangat (1992) randomization device by utilizing the Poisson distribution in survey sampling. It is shown that the proposed model is more efficient than Land etal. (2011) when the proportion of persons possessing a rare unrelated attribute is known. Properties of the proposed randomized response model have been studied along with recommendations. We have also extended the proposed model to stratified random sampling on the lines of Lee etal. (2013). It has been also shown that the proposed estimator is better than Lee etal.'s (2013) estimator. Numerical illustrations are also given in support of the present study.