Affiliations: School of Studies in Statistics, Vikram University, Ujjain, India
Corresponding author: Tanveer A. Tarray, School of Studies in Statistics, Vikram University, Ujjain 456010, India. E-mail: [email protected]
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. 
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.  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.