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This paper has great potential for estimating population proportion who possess stigmatized character by using Negative binomial distribution as a randomization device. The properties of the proposed estimation procedure have been examined. Measure of privacy protection for the proposed randomization device has been also quantified. Empirical studies are performed to support the theoretical results, which show the dominance of the proposed estimator over its competitors. Results are analysed and suitable recommendations are put forward for survey practitioners whenever they deal with sensitive characteristics.