A randomized response model for estimating a rare sensitive attribute in stratified sampling using poisson distribution

Abstract

The crux of this paper is to estimate the mean of the number of persons possessing a rare sensitive attribute based on the Singh et al. [1] randomization device by utilizing the Poisson distribution in stratified sampling. This study also deals with the extension of the estimation reported by Singh and Tarray [2] using a Poisson distribution and an unrelated question randomized response model reported in Singh et al. [1]. In stratified sampling, the estimators are proposed when the parameter of the rare unrelated attribute is known and also when it is unknown. It is shown that the proposed models are more efficient than the model given by Lee et al. [3] in both cases, that is, when the proportion of persons possessing a rare unrelated attribute is known and that when it is unknown. When the sizes of the stratified populations are not given, other estimators are suggested using stratified double sampling. Properties of the proposed randomized response model are studied and recommendations are made.