Development of an Improved Comprehensive Estimator for Population Proportion: Evidence from Radiation Data and Simulation Studies

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DOI: https://doi.org/10.28924/2291-8639-24-2026-192
Published: Jun 22, 2026
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Bassant Elkalzah, Yasser Salah S. Abougamea, Abdelfatah Abasher, Sohaib Ahmad, Mohammed Elgarhy, Development of an Improved Comprehensive Estimator for Population Proportion: Evidence from Radiation Data and Simulation Studies, Int. J. Anal. Appl., 24 (2026), 192.

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Bassant Elkalzah, Yasser Salah S. Abougamea, Abdelfatah Abasher, Sohaib Ahmad, Mohammed Elgarhy

Abstract

Accurate population proportion estimation is a fundamental requirement in survey sampling, practicality when direct measurement is limited by cost, time or other reasons. Use of auxiliary variable has been proposed as a feasible strategy for improving estimation efficiency. The purpose of this paper is to suggest an improved class of generalized estimators for population proportion using auxiliary attribute under simple random sampling without replacement. The proposed class of estimators is analytically derived under the minimum mean squared error criterion, and its theoretical properties such as bias and MSE are obtained up to the first order of approximation. To be specific, this general form is able to include such known estimators as special cases and therefore provides a unified and flexible estimation procedure. Comparative theoretical studies are established under which the new class has improved relative efficiency as compared to the usual estimators. To illustrate the empirical value of the proposed method, we apply it to actual radiation data and a simulation study is used. The empirical results indicate that the suggested estimators provide significant improvement in efficiency, especially when the auxiliary attribute are correlated with the study attribute. These findings emphasize that the estimator is robust and applicable to a variety of practical settings. The work highlights for the general statistical theory that estimation of population proportion may be improved by more effective use of auxiliary attributes.

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References

  1. S. Khan, M. Farooq, S. Ahmad, S. Khan, Improved Estimator for Estimation of Population Mean Using Predictive Approach Under PPS Sampling, VFAST Trans. Math. 12 (2024), 01–16. https://doi.org/10.21015/vtm.v12i2.1942.
  2. W.G. Cochran, The Estimation of the Yields of Cereal Experiments by Sampling for the Ratio of Grain to Total Produce, J. Agric. Sci. 30 (1940), 262–275. https://doi.org/10.1017/s0021859600048012.
  3. S. Bahl, R. Tuteja, Ratio and Product Type Exponential Estimators, J. Inf. Optim. Sci. 12 (1991), 159–164. https://doi.org/10.1080/02522667.1991.10699058.
  4. M.N. Murthy, Product Method of Estimation, Sankhya: Indian J. Stat. Ser. A (1964), 69–74.
  5. T.J. Rao, On Certail Methods of Improving Ration and Regression Estimators, Commun. Stat. - Theory Methods 20 (1991), 3325–3340. https://doi.org/10.1080/03610929108830705.
  6. S. Gupta, J. Shabbir, S. Ahmad, Estimation of Median in Two-Phase Sampling Using Two Auxiliary Variables, Commun. Stat. - Theory Methods 37 (2008), 1815–1822. https://doi.org/10.1080/03610920701826476.
  7. S.M. Alghamdi, S. Ahmad, S.M. Almarzouki, B. Aloraini, M.M. Badr, et al., Constructing a New Estimator for Estimating Population Mean Utilizing Auxiliary Information in Probability Proportional to Size Sampling, Alex. Eng. J. 110 (2025), 506–511. https://doi.org/10.1016/j.aej.2024.10.029.
  8. A. Abd-Elfattah, E. El-Sherpieny, S. Mohamed, O. Abdou, Improvement in Estimating the Population Mean in Simple Random Sampling Using Information on Auxiliary Attribute, Appl. Math. Comput. 215 (2010), 4198–4202. https://doi.org/10.1016/j.amc.2009.12.041.
  9. S. Bhushan, A. Kumar, Improved Estimation of Population Mean in Simple Random Sampling Using Attribute, Thailand Statistician 22 (2024), 374–389.
  10. S. Bhushan, A. Kumar, Evaluating the Performance of Logarithmic Type Estimators Using Auxiliary Attribute, Life Cycle Reliab. Saf. Eng. 12 (2023), 285–292. https://doi.org/10.1007/s41872-023-00236-4.
  11. S. Ahmad, J. Shabbir, Proportion Estimation Using Enhanced Class of Estimators Under Simple Random Sampling: Application with Real Data Sets and Simulation, Measurement: Interdiscip. Res. Perspect. 23 (2024), 297–309. https://doi.org/10.1080/15366367.2024.2346426.
  12. S. Bhushan, A. Kumar, S. Kumar, Efficient Classes of Estimators for Population Variance Using Attribute, Int. J. Math. Oper. Res. 22 (2022), 74–92. https://doi.org/10.1504/ijmor.2022.123124.
  13. M. Saini, B.R. Jitendrakumar, A. Kumar, Optimum Estimator in Simple Random Sampling Using Two Auxiliary Attributes with Application in Agriculture, Fisheries and Education Sectors, MethodsX 9 (2022), 101915. https://doi.org/10.1016/j.mex.2022.101915.
  14. H. Semary, S. Ahmad, I. Elbatal, C. Chesneau, M. Elgarhy, et al., New Comprehensive Class of Estimators for Population Proportion Using Auxiliary Attribute: Simulation and an Application, Alex. Eng. J. 99 (2024), 130–136. https://doi.org/10.1016/j.aej.2024.04.065.
  15. H.P. Singh, R.S. Solanki, Improved Estimation of Population Mean in Simple Random Sampling Using Information on Auxiliary Attribute, Appl. Math. Comput. 218 (2012), 7798–7812. https://doi.org/10.1016/j.amc.2012.01.047.
  16. T. Zaman, E. Toksoy, Improvement in Estimating the Population Mean in Simple Random Sampling Using Information on Two Auxiliary Attributes and Numerical Application in Agricultural Engineering, Fresenius Environ. Bull. 28 (2019), 4584–4590.
  17. S. Bhushan, A. Kumar, R. Gupta, Novel Logarithmic Estimator Using Two Auxiliary Attributes, Int. J. Agric. Stat. Sci. 18 (2022), 367.
  18. E. Zamanzade, X. Wang, Estimation of Population Proportion for Judgment Post-Stratification, Comput. Stat. Data Anal. 112 (2017), 257–269. https://doi.org/10.1016/j.csda.2017.03.016.
  19. E. Zamanzade, X. Wang, Proportion Estimation in Ranked Set Sampling in the Presence of Tie Information, Comput. Stat. 33 (2018), 1349–1366. https://doi.org/10.1007/s00180-018-0807-x.
  20. A.R. El-Saeed, S. Ahmad, B. Aloraini, Robust Estimator for Estimation of Population Mean Under PPS Sampling: Application to Radiation Data, J. Radiat. Res. Appl. Sci. 18 (2025), 101384. https://doi.org/10.1016/j.jrras.2025.101384.
  21. B. Aloraini, L. Diab, S. Ahmad, Regression Cum Exponential Type Estimator for Population Proportion Using Auxiliary Attributes: Application on Radiation Data and Simulation Study, J. Radiat. Res. Appl. Sci. 18 (2025), 101479. https://doi.org/10.1016/j.jrras.2025.101479.
  22. G. Alomani, M. Kayid, S. Ahmad, Application to Radiation Data Sets by Suggesting an Improved Mean Estimator Under Probability Proportional to Size Sampling, J. Radiat. Res. Appl. Sci. 18 (2025), 101354. https://doi.org/10.1016/j.jrras.2025.101354.
  23. T. Zaman, New Family of Estimators Using Two Auxiliary Attributes, Int. J. Adv. Res. Eng. Manage. 4 (2018), 11–16.
  24. T. Zaman, C. Kadilar, Novel Family of Exponential Estimators Using Information of Auxiliary Attribute, J. Stat. Manag. Syst. 22 (2019), 1499–1509. https://doi.org/10.1080/09720510.2019.1621488.
  25. B. Prasad, Some Unbiased Estimators Versus Mean Per Unit and Ratio Estimators in Finite Population Sample Surveys, Commun. Stat. - Theory Methods 15 (1986), 3647–3657. https://doi.org/10.1080/03610928608829338.
  26. R. Singh, H.P. Singh, M. Espejo, The Efficiency of an Alternative to Ratio Estimator Under a Super Population Model, J. Stat. Plan. Inference 71 (1998), 287–301. https://doi.org/10.1016/s0378-3758(98)00009-3.
  27. M. Khoshnevisan, R. Singh, P. Chauhan, N. Sawan, F. Smarandache, A General Family of Estimators for Estimating Population Mean Using Known Value of Some Population Parameter(s), Far East J. Theor. Stat. 22 (2007), 181–191.