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Dual Transformation of Auxiliary Variables by Using Outliers in Stratified Random Sampling

Author

Listed:
  • Mohammed Ahmed Alomair

    (Department of Quantitative Methods, School of Business, King Faisal University, Al-Ahsa 31982, Saudi Arabia
    These authors contributed equally to this work.)

  • Umer Daraz

    (School of Mathematics and Statistics, Central South University, Changsha 410017, China
    These authors contributed equally to this work.)

Abstract

To estimate the finite population variance of the study variable, this paper proposes an improved class of efficient estimators using different transformations. When both the minimum and maximum values of the auxiliary variable are known and the ranks of the auxiliary variable are associated with the study variable, these estimators are particularly useful. Therefore, the precision of the estimators can be effectively improved through the utilization of these rankings. We examine the properties of the proposed class of estimators, including bias and mean squared error (MSE), using a first-order approximation through a stratified random sampling method. To determine the performances and validate the findings mathematically, a simulation study is carried out. Based on the results, the proposed class of estimators performs better in terms of the mean squared error ( M S E ) and percent relative efficiency ( P R E ) as compared to other estimators in all scenarios. Furthermore, in order to prove that the performances of the improved class of estimators are better than those of the existing estimators, three data sets are examined in the application section.

Suggested Citation

  • Mohammed Ahmed Alomair & Umer Daraz, 2024. "Dual Transformation of Auxiliary Variables by Using Outliers in Stratified Random Sampling," Mathematics, MDPI, vol. 12(18), pages 1-16, September.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:18:p:2839-:d:1477043
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    References listed on IDEAS

    as
    1. Tolga Zaman & Hasan Bulut, 2023. "An efficient family of robust-type estimators for the population variance in simple and stratified random sampling," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 52(8), pages 2610-2624, April.
    2. Housila Singh & Ramkrishna Solanki, 2013. "A new procedure for variance estimation in simple random sampling using auxiliary information," Statistical Papers, Springer, vol. 54(2), pages 479-497, May.
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