Partial Randomized Response Model for Estimating a Rare Sensitive Attribute in Probability Proportional to Size Measures Using Poisson Distribution

Abstract

In this paper motivated by Lee et al (2013) and Singh et al (2017,2020), we have suggested the estimation procedures of mean number of persons possessing sensitive attribute using Narjis and Shabbir (2020) randomized response model for the population which comprises of some clusters and the population is stratified with some clusters in each stratum. The estimator for the mean number of persons possessing sensitive attribute under a Poisson distribution, its variance, and the estimator of the variance are proposed under two-stage and stratified two-stage sampling schemeswhen the parameter of the rare sensitive attribute is pretended to be known and unknown. We employ the sampling scheme with probability proportional to size to select the first-stage units and simple random sampling with replacement to select the second-stage units.Theperformance of the suggested estimation procedures are demonstrated through numerical illustration over Singh and Suman (2019) estimators.