Journal of Statistics Applications & Probability


The estimated mean of the number of individuals holding a rare sensitive attribute (e.g., illegal use of tax evasion, narcotics, domestic abuse, or illicit income) in the population spread over a broad geographical region through traditional sampling structures is difficult to quantify because of the social, political and security circumstances which typically contribute to their concentration in some geographical region. In this paper, The mean of the number of persons possessing a rare sensitive attribute (MNSA) by utilizing the Poisson distribution is estimated using a modified Horvitz-Thompson type of estimator under an adaptive two-stage cluster sampling scheme when an unrelated rare non-sensitive attribute parameter is either known or unknown. The variances of the resultant estimators and their unbiased estimates are expressed. In a small example from the variances and mean squared errors, one sees that the adaptive design with the estimator has the lowest variance compared to the unbiased strategy.

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