Estimation of the finite population mean using extreme values and ranks of the auxiliary variable in two-phase sampling

Hleil Alrweili; Fatimah A. Almulhim; Hleil Alrweili; Fatimah A. Almulhim

doi:10.3934/math.2025403

AIMS Mathematics

2025, Volume 10, Issue 4: 8794-8817. doi: 10.3934/math.2025403

Previous Article Next Article

Research article Special Issues

Estimation of the finite population mean using extreme values and ranks of the auxiliary variable in two-phase sampling

Hleil Alrweili ^{1
,},
Fatimah A. Almulhim ^{2
,
,}

1.
Department of Mathematics, College of Science, Northern Border University, Arar, Saudi Arabia; hleil.alrweili@nbu.edu.sa
2.
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P. O. Box 84428, Riyadh 11671, Saudi Arabia

Received: 12 March 2025 Revised: 08 April 2025 Accepted: 11 April 2025 Published: 17 April 2025
MSC : 62D

This study aimed to improve the estimation of the mean of the dependent variable by incorporating the smallest and largest values and ranks of the independent variable. To achieve this, we introduce two new classes of estimators that offer enhanced accuracy compared with the existing approaches, as evaluated using the mean squared error (MSE) criterion. The key features of the proposed estimators are examined through a first-order approximation method, particularly focusing on the bias and mean squared error under two-phase sampling. In addition, their performance is assessed using simulated populations generated from six different distributions with varying parameter settings, along with three real datasets. Furthermore, the findings show that the new estimators achieve lower mean squared errors compared with existing methods.
- two-phase sampling,
- largest and smallest values,
- ranks,
- bias,
- mean squared error
Citation: Hleil Alrweili, Fatimah A. Almulhim. Estimation of the finite population mean using extreme values and ranks of the auxiliary variable in two-phase sampling[J]. AIMS Mathematics, 2025, 10(4): 8794-8817. doi: 10.3934/math.2025403

Related Papers:

Abstract

This study aimed to improve the estimation of the mean of the dependent variable by incorporating the smallest and largest values and ranks of the independent variable. To achieve this, we introduce two new classes of estimators that offer enhanced accuracy compared with the existing approaches, as evaluated using the mean squared error (MSE) criterion. The key features of the proposed estimators are examined through a first-order approximation method, particularly focusing on the bias and mean squared error under two-phase sampling. In addition, their performance is assessed using simulated populations generated from six different distributions with varying parameter settings, along with three real datasets. Furthermore, the findings show that the new estimators achieve lower mean squared errors compared with existing methods.

References

[1]	W. G. Cochran, Sampling techniques, 2 Eds., Hoboken: John Wiley and Sons, 1963.
[2]	C. E. Särndal, Sample survey theory vs. general statistical theory: estimation of the population mean, Int. Stat. Rev., 40 (1972), 1–12. https://doi.org/10.2307/1402700 doi: 10.2307/1402700
[3]	S. Y. Yang, D. B. Meng, H. F. Yang, C. Q. Luo, X. Y. Su, Enhanced soft Monte Carlo simulation coupled with support vector regression for structural reliability analysis, P. I. Civil Eng.-Transp., 2024 (2024), 1–16. https://doi.org/10.1680/jtran.24.00128 doi: 10.1680/jtran.24.00128
[4]	B. V. Sukhatme, Some ratio-type estimators in two-phase sampling, J. Am. Stat. Assoc., 57 (1962), 628–632. https://doi.org/10.2307/2282400 doi: 10.2307/2282400
[5]	A. Y. Erinola, R. V. K. Singh, A. Audu, T. James, Modified class of estimator for finite population mean under two-phase sampling using regression estimation approach, Asian Journal of Probability and Statistics, 14 (2021), 52–64. https://doi.org/10.9734/ajpas/2021/v14i430338 doi: 10.9734/ajpas/2021/v14i430338
[6]	S. Guha, H. Chandra, Improved estimation of finite population mean in two-phase sampling with subsampling of the nonrespondents, Math. Popul. Stud., 28 (2021), 24–44. https://doi.org/0.1080/08898480.2019.1694325
[7]	A. Kamal, N. Amir, H. Dastagir, Some exponential type predictive estimators of finite population mean in two-phase sampling, Journal of Statistics, Computing and Interdisciplinary Research, 2 (2020), 51–57. https://doi.org/10.52700/scir.v2i1.10 doi: 10.52700/scir.v2i1.10
[8]	T. Zaman, C. Kadilar, New class of exponential estimators for finite population mean in two-phase sampling, Commun. Stat.-Theor. M., 50 (2019), 874–889. https://doi.org/10.1080/03610926.2019.1643480 doi: 10.1080/03610926.2019.1643480
[9]	S. Mohanty, J. Sahoo, A note on improving the ratio method of estimation through linear transformation using certain known population parameters, Sankhya: The Indian Journal of Statistics, 57 (1995), 93–102.
[10]	M. Khan, J. Shabbir, Some improved ratio, product, and regression estimators of finite population mean when using minimum and maximum values, Sci. World J., 2013 (2013), 431868. https://doi.org/10.1155/2013/431868 doi: 10.1155/2013/431868
[11]	M. Khan, Improvement in estimating the finite population mean under maximum and minimum values in double sampling scheme, J. Stat. Appl. Pro. Lett., 2 (2015), 115–121.
[12]	G. S. Walia, H. Kaur, M. K. Sharma, Ratio type estimator of population mean through efficient linear transformation, American Journal of Mathematics and Statistics, 5 (2015), 144–149. https://doi.org/10.5923/j.ajms.20150503.06 doi: 10.5923/j.ajms.20150503.06
[13]	U. Daraz, J. Shabbir, H. Khan, Estimation of finite population mean by using minimum and maximum values in stratified random sampling, J. Mod. Appl. Stat. Meth., 17 (2018), eP2548. https://doi.org/10.22237/jmasm/1532007537 doi: 10.22237/jmasm/1532007537
[14]	U. Daraz, M. Khan, Estimation of variance of the difference-cum-ratio-type exponential estimator in simple random sampling, RMS Res. Math. Stat., 8 (2021), 1899402. https://doi.org/10.1080/27658449.2021.1899402 doi: 10.1080/27658449.2021.1899402
[15]	U. Daraz, M. A. Alomair, O. Albalawi, Variance estimation under some transformation for both symmetric and asymmetric data, Symmetry, 16 (2024), 957. https://doi.org/10.3390/sym16080957 doi: 10.3390/sym16080957
[16]	A. S. Alghamdi, H. Alrweili, A comparative study of new ratio-type family of estimators under stratified two-phase sampling, Mathematics, 13 (2025), 327. https://doi.org/10.3390/math13030327 doi: 10.3390/math13030327
[17]	U. Daraz, J. B. Wu, D. Agustiana, W. Emam, Finite population variance estimation using Monte Carlo simulation and real life application, Symmetry, 17 (2025), 84. https://doi.org/10.3390/sym17010084 doi: 10.3390/sym17010084
[18]	U. Daraz, D. Agustiana, J. B. Wu, W. Emam, Twofold auxiliary information under two-Phase sampling: An improved family of double-transformed variance estimators, Axioms, 14 (2025), 64. https://doi.org/10.3390/axioms14010064 doi: 10.3390/axioms14010064
[19]	C. X. Long, W. X. Chen, R. Yang, D. S. Yao, Ratio estimation of the population mean using auxiliary information under the optimal sampling design, Probab. Eng. Inform. Sc., 36 (2022), 449–460. https://doi.org/10.1017/S0269964820000625 doi: 10.1017/S0269964820000625
[20]	H. O. Cekim, H. Cingi, Some estimator types for population mean using linear transformation with the help of the minimum and maximum values of the auxiliary variable, Hacet. J. Math. Stat., 46 (2017), 685–694. https://doi.org/10.15672/HJMS.201510114186 doi: 10.15672/HJMS.201510114186
[21]	S. Chatterjee, A. S. Hadi, Regression analysis by example, 5 Eds., Hoboken: John Wiley & Sons, 2013.
[22]	A. S. Alghamdi, H. Alrweili, New class of estimators for finite population mean under stratified double phase sampling with simulation and real-life application, Mathematics, 13 (2025), 329. https://doi.org/10.3390/math13030329 doi: 10.3390/math13030329
[23]	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.
[24]	H. P. Singh, M. R. Espeio, Double sampling ratio-product estimator of a finite population mean in sample surveys, J. Appl. Stat., 34 (2007), 71–85. https://doi.org/10.1080/02664760600994562 doi: 10.1080/02664760600994562
[25]	U. Daraz, J. B. Wu, O. Albalawi, Double exponential ratio estimator of a finite population variance under extreme values in simple random sampling, Mathematics, 12 (2024), 1737. https://doi.org/10.3390/math12111737 doi: 10.3390/math12111737
[26]	U. Daraz, J. B. Wu, M. A. Alomair, L. A. Aldoghan, New classes of difference cum-ratio-type exponential estimators for a finite population variance in stratified random sampling, Heliyon, 10 (2024), e33402. https://doi.org/10.1016/j.heliyon.2024.e33402 doi: 10.1016/j.heliyon.2024.e33402
[27]	M. A. Alomair, U. Daraz, Dual transformation of auxiliary variables by using outliers in stratified random sampling, Mathematics, 12 (2024), 2839. https://doi.org/10.3390/math12182839 doi: 10.3390/math12182839
[28]	U. Daraz, M. A. Alomair, O. Albalawi, A. S. Al Naim, New techniques for estimating finite population variance using ranks of auxiliary variable in two-stage sampling, Mathematics, 12 (2024), 2741. https://doi.org/10.3390/math12172741 doi: 10.3390/math12172741
[29]	Punjab Development Statistics, Bureau of Statistics, Government of the Punjab: Lahore, Pakistan, 2013. Available from: https://bos.punjab.gov.pk.

Reader Comments

Your name:*

Email:*
© 2025 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)