Enhanced Logarithmic-Type Estimators for Estimation ofPopulation Variance Under Simple Random SamplingFramework: Computational Analysis andSimulation Evidence

  • Authors

    • Anchal Yadav Department of Statistics, University of Lucknow, Lucknow-226007, Uttar Pradesh, India
    • Mukesh Kumar Department of Statistics, University of Lucknow, Lucknow-226007, Uttar Pradesh, India
    https://doi.org/10.14419/y58gth40

    Received date: February 27, 2026

    Accepted date: April 19, 2026

    Published date: April 22, 2026

  • Auxiliary Information; Logarithmic-Type Estimators; Mean Squared Error; Bias; Simple Random ‎Sampling

  • Abstract

    Survey sampling continues to play a pivotal role in modern statistical research, offering a ‎efficient means of estimating population parameters without requiring a complete enumeration. ‎However, practical data collection frequently involves extreme or atypical observations that, if ‎overlooked, can distort estimation accuracy and lead to biased conclusions. The former research ‎primarily focuses on use of auxiliary information to estimate the population parameters of main ‎variable. The class of estimators suggested in this category one ratio type estimators, product type ‎estimators and regression type estimators. Later, Bahl and Tuteja (1991) suggested a new class of ‎exponential and product estimators. Recent advancements have introduced logarithmic-type ‎estimators, but their statistical properties remain only partially explored. Recognizing this ‎challenge, the present study proposes a refined logarithmic-type estimator for finite population ‎variance within the framework of simple random sampling without replacement (SRSWOR). The ‎estimator incorporates auxiliary information to improve the precision and stability of variance ‎estimation. Theoretical properties, including bias and mean squared error (MSE), are derived up ‎to the first order of approximation, ensuring a rigorous analytical foundation. To assess its ‎performance, comparative and simulation-based analyses are carried out against several existing ‎estimators. The findings reveal that the proposed estimator consistently produces lower MSE ‎values and exhibits greater robustness. These results confirm both the theoretical and empirical ‎superiority of the proposed approach. Overall, the study contributes to the growing body of ‎literature on efficient estimation techniques by presenting a more accurate and reliable alternative ‎for population variance estimation in survey sampling and their applications‎.

  • References

    1. C. T. Isaki, “Variance estimation using auxiliary information,” J. Amer. Stat. Assoc., vol. 78, no. 381, pp. 117–123, 1983, https://doi.org/10.1080/01621459.1983.10477939.
    2. S. Bahl and R. K. Tuteja, “Ratio and product type exponential estimators,” J. Inf. Optim. Sci., vol. 12, no. 1, pp. 159–164, Jan. 1991, https://doi.org/10.1080/02522667.1991.10699058.
    3. M. R. Garcia and A. A. Cebrian, “Repeated substitution method: The ratio estimator for the population variance,” Metrika, vol. 43, no. 1, pp. 101–105, Dec. 1996, https://doi.org/10.1007/BF02613900.
    4. L. N. Upadhyaya and H. P. Singh, “Use of transformed auxiliary variable in estimating the finite population mean,” Biometrical J., vol. 41, no. 5, pp. 627–636, 1999. https://doi.org/10.1002/(SICI)1521-4036(199909)41:5<627::AID-BIMJ627>3.3.CO;2-N.
    5. L. N. Upadhyaya, H. P. Singh, and S. Singh, “A class of estimators for estimating the variance of the ratio estimator,” J. Jpn. Stat. Soc., vol. 34, no. 1, pp. 47–63, 2004. https://doi.org/10.14490/jjss.34.47.
    6. P. Chandra and H. P. Singh, “A family of estimators for population variance using knowledge of kurtosis of an auxiliary variable in sample survey,” Stat. Transit., vol. 7, no. 1, pp. 27–34, 2005.
    7. A. Arcos, M. Rueda, M. D. Martínez, S. González, and Y. Román, “Incorporating the auxiliary information available in variance estimation,” Appl. Math. Comput., vol. 160, no. 2, pp. 387–399, 2005. https://doi.org/10.1016/j.amc.2003.11.010.
    8. C. Kadilar and H. Cingi, “New ratio estimators using correlation coefficient,” InterStat, vol. 4, pp. 1–11, Mar. 2006.
    9. H. P. Singh and R. S. Solanki, “A new procedure for variance estimation in simple random sampling using auxiliary information,” Stat. Papers, vol. 54, no. 2, pp. 479–497, May 2013, https://doi.org/10.1007/s00362-012-0445-2.
    10. S. K. Yadav, C. Kadilar, J. Shabbir, and S. Gupta, “Improved family of estimators of population variance in simple random sampling,” J. Stat. The-ory Pract., vol. 9, no. 2, pp. 219–226, Apr. 2015, https://doi.org/10.1080/15598608.2013.856359.
    11. J. Shabbir and S. Gupta, “Some estimators of finite population variance of stratified sample mean,” Commun. Stat. Theory Methods, vol. 39, no. 16, pp. 3001–3008, Aug. 2010, https://doi.org/10.1080/03610920903170384.
    12. G. N. Singh and M. Khalid, “Effective estimation strategy of population variance in two-phase successive sampling under random non-response,” J. Stat. Theory Pract., vol. 13, no. 1, p. 4, Mar. 2019, https://doi.org/10.1007/s42519-018-0010-y.
    13. H. O. Cekim and C. Kadilar, “ln-type variance estimators in simple random sampling,” Pak. J. Stat. Oper. Res., pp. 689–696, Dec. 2020, https://doi.org/10.18187/pjsor.v16i4.3072.
    14. A. Audu, M. D. Kareem, J. N. Eze, and U. Daraz, “Difference-cum-ratio estimators for estimating finite population coefficient of variation in sim-ple random sampling,” Asian J. Probab. Stat., vol. 13, no. 3, pp. 13–29, 2021. https://doi.org/10.9734/ajpas/2021/v13i330308.
    15. U. Daraz and M. Khan, “Estimation of variance of the difference-cum-ratio-type exponential estimator in simple random sampling,” Res. Math. Stat., vol. 8, no. 1, p. 1899402, Jan. 2021, https://doi.org/10.1080/27658449.2021.1899402.
    16. S. Ahmad, M. Khan, U. Daraz, and M. Nawaz, “A simulation study: Improved ratio-in-regression type variance estimator based on dual use of aux-iliary variable under simple random sampling,” PLoS One, vol. 17, no. 11, p. e0276540, 2022. https://doi.org/10.1371/journal.pone.0276540.
    17. U. Daraz, J. Wu, and O. Albalawi, “Double exponential ratio estimator of a finite population variance under extreme values in simple random sam-pling,” Mathematics, vol. 12, p. 1737, 2024. https://doi.org/10.3390/math12111737
    18. N. K. Adichwal, P. Sharma, and R. Singh, “Generalized class of estimators for population variance using information on two auxiliary variables,” Int. J. Appl. Comput. Math., vol. 3, no. 2, pp. 651–661, Jun. 2017, https://doi.org/10.1007/s40819-015-0119-6.
    19. R. Gupta, S. K. Yadav, M. Ali, and G. Kumar, “Improved estimation of the population mean by integrating additional auxiliary parameters,” Kore-an J. Physiol. Pharmacol., vol. 28, no. 1, pp. 205–210, Jan. 2024, https://doi.org/10.36106/ijar/7104032.
    20. A. Adejumobi, M. . Abiodun Yunusa, Y. . A. Erinola, and K. . Abubakar, “An Efficient Logarithmic Ratio Type Estimator of Finite Population Mean under Simple Random Sampling”, International Journal of Engineering and Applied Physics, vol. 3, no. 2, pp. 700–705, May 2023.
    21. R. A. Robb, “W. G. Cochran, Sampling Techniques, John Wiley & Sons, 1963, ix + 413 pp., 72 s.,” Proc. Edinb. Math. Soc., vol. 13, no. 4, pp. 342–343, 1963. https://doi.org/10.1017/S0013091500025724.
    22. J. Subramani and G. Kumarapandiyan, “Variance estimation using quartiles and their functions of an auxiliary variable,” Ratio J., vol. 1, no. 1, 2012. https://doi.org/10.5923/j.ijps.20120103.02.

  • Downloads