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AIMS Mathematics

2025, Volume 10, Issue 4: 8907-8925. doi: 10.3934/math.2025408
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Research article

Developing and evaluating efficient estimators for finite population mean in two-phase sampling

  • 1.
    Department of Statistics University of Peshawar, Pakistan
  • 2.
    Department of Statistics The Islamia University Bahawalpur, Punjab Pakistan
  • 3.
    Department of Industrial Engineering, King Saud University Riyadh 12372, Saudi Arabia
  • 4.
    Department of Statistics, Faculty of Science, University of Tabuk Saudi Arabia
  • Received: 05 March 2025 Revised: 05 April 2025 Accepted: 09 April 2025 Published: 18 April 2025

  • MSC : 62DXX

  • The estimator development process is more efficient when additional information is used. However, occasionally, it is necessary to use information regarding unknown population parameters. In these cases, we chose two-phase sampling by substituting the population mean of the supplemental variable with the sample mean from first-phase sampling. The goal of this project was to develop effective estimators of the finite population mean in a two-phase sampling scenario with a single auxiliary variable. Under certain conditions, the recommended estimators outperform the current estimators, producing biased and Mean Square Error (MSE) expressions. Empirical and theoretical comparisons of the proposed families were conducted using real and simulated data. We found that the proposed families were more effective in the two-phase sampling situation than in all-population mean estimators.

    Citation: Khazan Sher, Muhammad Ameeq, Sidra Naz, Basem A. Alkhaleel, Muhammad Muneeb Hassan, Olayan Albalawi. Developing and evaluating efficient estimators for finite population mean in two-phase sampling[J]. AIMS Mathematics, 2025, 10(4): 8907-8925. doi: 10.3934/math.2025408

    Related Papers:

  • The estimator development process is more efficient when additional information is used. However, occasionally, it is necessary to use information regarding unknown population parameters. In these cases, we chose two-phase sampling by substituting the population mean of the supplemental variable with the sample mean from first-phase sampling. The goal of this project was to develop effective estimators of the finite population mean in a two-phase sampling scenario with a single auxiliary variable. Under certain conditions, the recommended estimators outperform the current estimators, producing biased and Mean Square Error (MSE) expressions. Empirical and theoretical comparisons of the proposed families were conducted using real and simulated data. We found that the proposed families were more effective in the two-phase sampling situation than in all-population mean estimators.



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    [1] H. P. Singh, G. K. Vishwakarma, Modified exponential ratio and product estimators for finite population mean in double sampling, Aust. J. Stat., 36 (2007), 217–225. https://doi.org/10.17713/ajs.v36i3.333 doi: 10.17713/ajs.v36i3.333
    [2] L. K. Grover, P. Kaur, G. K. Vishawkarma, Product type exponential estimators of population mean under linear transformation of auxiliary variable in simple random sampling, Appl. Math. Comput., 219 (2012), 1937–1946. https://doi.org/10.1016/j.amc.2012.08.036 doi: 10.1016/j.amc.2012.08.036
    [3] M. Noor-ul-Amin, M. Hanif, Some exponential estimators in survey sampling, Pak. J. Stat., 28 (2012).
    [4] K. Sher, M. Ameeq, M. M. Hassan, O. Albalawi, A. Afzal, Development of improved estimators of finite population mean in simple random sampling with dual auxiliaries and its application to real world problems, Heliyon, 10 (2024). https://doi.org/10.1016/j.heliyon.2024.e30991 doi: 10.1016/j.heliyon.2024.e30991
    [5] S. Muneer, J. Shabbir, A. Khalil, Estimation of finite population mean in simple random sampling and stratified random sampling using two auxiliary variables, Commun. Stat.-Theor. M., 46 (2017), 2181–2192. https://doi.org/10.1080/03610926.2015.1035394 doi: 10.1080/03610926.2015.1035394
    [6] S. Choudhury, B. K. Singh, A class of product-cum-dual to product estimators of the population mean in survey sampling using auxiliary information, Asian J. Math. Stat., 6 (2012). https://doi.org/10.3923/ajms.2012 doi: 10.3923/ajms.2012
    [7] A. K. Sabat, R. K. Sahoo, L. N. Sahoo, Composite ratio estimators in a two-phase sampling using multiple additional supplementary variables, Far East J. Appl. Math., 117 (2024), 49–66. https://doi.org/10.17654/0972096024003 doi: 10.17654/0972096024003
    [8] C. Di Gravio, J. S. Schildcrout, R. Tao, Efficient designs and analysis of two-phase studies with longitudinal binary data, Biometrics, 80 (2024). https://doi.org/10.1093/biomtc/ujad010 doi: 10.1093/biomtc/ujad010
    [9] T. Zaman, C. Kadilar, New class of exponential estimators for finite population mean in two-phase sampling, Commun. Stat.-Theor. M., 50 (2021), 874–889. https://doi.org/10.1080/03610926.2019.1643480 doi: 10.1080/03610926.2019.1643480
    [10] Y. Tato, B. K. Singh, Exponential chain dual to ratio cum dual to product estimator for finite population mean in double sampling scheme, Appl. Appl. Math., 12 (2017), 4.
    [11] P. Misra, Regression type double sampling estimator of population mean using auxiliary information, J. Reliab. Stat. Stud., 2018, 21–28.
    [12] M. Kumar, S. Bahl, Class of dual to ratio estimators for double sampling, Stat. Pap., 47 (2006), 319. https://doi.org/10.1007/s00362-005-0291-6 doi: 10.1007/s00362-005-0291-6
    [13] S. K. Yadav, S. Gupta, S. S. Mishra, A. K. Shukla, Modified ratio and product estimators for estimating population mean in two-phase sampling, Am. J. Oper. Res., 6 (2016), 61–68. https://doi.org/10.5923/j.ajor.20160603.02 doi: 10.5923/j.ajor.20160603.02
    [14] N. Ozgul, H. Cingi, A new class of exponential regression cum ratio estimator in two phase sampling, Hacet. J. Math. Stat., 43 (2014), 131–140.
    [15] J. Shabbir, S. Gupta, R. Onyango, On using the conventional and nonconventional measures of the auxiliary variable for mean estimation, Math. Probl. Eng., 2021 (2021), 3741620. https://doi.org/10.1155/2021/3741620 doi: 10.1155/2021/3741620
    [16] S. Gupta, J. Shabbir, On improvement in estimating the population mean in simple random sampling, J. Appl. Stat., 35 (2008), 559–566. https://doi.org/10.1080/02664760701835839 doi: 10.1080/02664760701835839
    [17] J. Shabbir, S. Gupta, On estimating finite population mean in simple and stratified random sampling, Commun. Stat.-Theor. M., 40 (2010), 199–212. https://doi.org/10.1080/03610920903411259 doi: 10.1080/03610920903411259
    [18] W. G. Cochran, Sampling techniques, 3Eds., New York: John Wiley & Sons, 1977.
    [19] D. Singh, F. S. Chaudhary, Theory and analysis of sample survey design, New Delhi: New Age International Publishers, 1986.
    [20] R. Singh, N. S. Mangat, Elements of survey sampling, Springer Science & Business Media, 15 (2013).
    [21] A. K. Das, Contributions to the theory of sampling strategies based on auxiliary information, Ph.D. Thesis, Bidhan Chandra Krishi Vishwavidyalaya, 1988.
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