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Double Exponential Ratio Estimator of a Finite Population Variance under Extreme Values in Simple Random Sampling

Author

Listed:
  • Umer Daraz

    (School of Mathematics and Statistics, Central South University, Changsha 410017, China)

  • Jinbiao Wu

    (School of Mathematics and Statistics, Central South University, Changsha 410017, China)

  • Olayan Albalawi

    (Department of Statistics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia)

Abstract

This article presents an improved class of efficient estimators aimed at estimating the finite population variance of the study variable. These estimators are especially useful when we have information about the minimum/maximum values of the auxiliary variable within a framework of simple random sampling. The characteristics of the proposed class of estimators, including bias and mean squared error ( M S E ) under simple random sampling are derived through a first-order approximation. To assess the performance and validate the theoretical outcomes, we conduct a simulation study. Results indicate that the proposed class of estimators has lower M S E s as compared to other existing estimators across all simulation scenarios. Three datasets are used in the application section to emphasize the effectiveness of the proposed class of estimators over conventional unbiased variance estimators, ratio and regression estimators, and other existing estimators.

Suggested Citation

  • Umer Daraz & Jinbiao Wu & Olayan Albalawi, 2024. "Double Exponential Ratio Estimator of a Finite Population Variance under Extreme Values in Simple Random Sampling," Mathematics, MDPI, vol. 12(11), pages 1-11, June.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:11:p:1737-:d:1407828
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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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