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A Probability Proportional to Size Estimation of a Rare Sensitive Attribute Using a Partial Randomized Response Model with Poisson Distribution

Author

Listed:
  • Gi-Sung Lee

    (Department of Children Welfare, Woosuk University, Wanju 55338, Republic of Korea)

  • Ki-Hak Hong

    (Department of Computer Science, Dongshin University, Naju 58245, Republic of Korea)

  • Chang-Kyoon Son

    (Department of Applied Statistics, Dongguk University, Gyeongju 38066, Republic of Korea)

Abstract

In this paper, we suggest using a partial randomized response model using Poisson distribution to efficiently estimate a rare sensitive attribute by applying the probability proportional to size (PPS) sampling method when the population is composed of several different and sensitive clusters. We have obtained estimators for a rare and sensitive attribute and their variances and variance estimates by applying PPS sampling and two-stage equal probability sampling. We compare the efficiency between the estimators of the rare sensitive attribute, one obtained via PPS sampling with replacement and the other obtained using the two-stage equal probability sampling with replacement. As a result, it is confirmed that the estimate obtained via the PPS sampling with replacement is more efficient than the estimate provided by the two-stage equal probability sampling with replacement when the cluster sizes are different.

Suggested Citation

  • Gi-Sung Lee & Ki-Hak Hong & Chang-Kyoon Son, 2024. "A Probability Proportional to Size Estimation of a Rare Sensitive Attribute Using a Partial Randomized Response Model with Poisson Distribution," Mathematics, MDPI, vol. 12(2), pages 1-11, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:2:p:196-:d:1314598
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    References listed on IDEAS

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    1. Ghulam Narjis & Javid Shabbir, 2021. "An efficient partial randomized response model for estimating a rare sensitive attribute using Poisson distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(1), pages 1-17, January.
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