Abstract
The crux of this paper is to estimate the mean of the number of persons possessing a rare sensitive attribute based on Singh et al. [24] randomization device by utilizing the Poisson distribution in survey sampling. It is also shown that the proposed models are more efficient than Land et al. [6] in both the cases when the proportion of persons possessing a rare unrelated attribute is known and that when it is unknown. Properties of the proposed randomized response model have been studied along with recommendations. Numerical illustrations are also given in support of the present study.