Efficient classes of estimators for estimating indeterminate population mean using neutrosophic ranked set sampling

Anoop Kumar; Priya; Abdullah Mohammed Alomair; Anoop Kumar; Priya; Abdullah Mohammed Alomair

doi:10.3934/math.2025410

AIMS Mathematics

2025, Volume 10, Issue 4: 8946-8964. doi: 10.3934/math.2025410

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Research article

Efficient classes of estimators for estimating indeterminate population mean using neutrosophic ranked set sampling

1.
Department of Statistics, Central University of Haryana, Mahendergarh, Haryana 123031, India
2.
Department of Quantitative Methods, School of Business, King Faisal University, Al-Ahsa 31982, Saudi Arabia

Received: 15 January 2025 Revised: 26 March 2025 Accepted: 08 April 2025 Published: 18 April 2025
MSC : 62D05

Estimating the population mean with accuracy is frequently challenged by uncertain and inaccurate data in survey sampling. This study presents some efficient classes of estimators for estimating the indeterminate population mean using neutrosophic ranked set sampling (NRSS). The study establishes the bias and mean squared error (MSE) of the suggested estimators and compares their performance with the existing neutrosophic estimators. Analytical comparisons show considerable efficiency benefits over the existing neutrosophic estimators. Simulation research and executions on real-life datasets confirm the accuracy of the proposed neutrosophic estimators when dealing with uncertainty. The findings highlight the potential of proposed NRSS estimators as a powerful tool for population mean estimation by providing new insights into statistical methodologies for uncertain and imprecise situations.
- mean square error,
- neutrosophic ranked set sampling,
- efficient classes of estimators,
- efficiency,
- indeterminacy
Citation: Anoop Kumar, Priya, Abdullah Mohammed Alomair. Efficient classes of estimators for estimating indeterminate population mean using neutrosophic ranked set sampling[J]. AIMS Mathematics, 2025, 10(4): 8946-8964. doi: 10.3934/math.2025410

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Abstract

Estimating the population mean with accuracy is frequently challenged by uncertain and inaccurate data in survey sampling. This study presents some efficient classes of estimators for estimating the indeterminate population mean using neutrosophic ranked set sampling (NRSS). The study establishes the bias and mean squared error (MSE) of the suggested estimators and compares their performance with the existing neutrosophic estimators. Analytical comparisons show considerable efficiency benefits over the existing neutrosophic estimators. Simulation research and executions on real-life datasets confirm the accuracy of the proposed neutrosophic estimators when dealing with uncertainty. The findings highlight the potential of proposed NRSS estimators as a powerful tool for population mean estimation by providing new insights into statistical methodologies for uncertain and imprecise situations.

References

[1]	W. G. Cochran, The estimation of the yields of the 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 doi: 10.1017/S0021859600048012
[2]	M. N. Murthy, Product method of estimation, Sankhya Indian J. St. Ser. A, 26 (1964), 69–74. Available from: https://www.jstor.org/stable/25049308.
[3]	B. V. S. Sisodia, V. K. Dwivedi, A modified ratio estimator using coefficient of variation of auxiliary variable, J. Indian Soc. Agri. Stat., 33 (1981), 13–18.
[4]	L. N. Upadhyaya, H. P. Singh, Use of transformed auxiliary variable in estimating the finite population mean, Biometrical J., 41 (1999), 627–636. https://doi.org/10.1002/(SICI)1521-4036(199909)41:5<3C627::AID-BIMJ627>3E3.0.CO;2-W doi: 10.1002/(SICI)1521-4036(199909)41:5<3C627::AID-BIMJ627>3E3.0.CO;2-W
[5]	S. Hussain, S. Ahmad, M. Saleem, S. Akhtar, Finite population distribution function estimation with dual use of auxiliary information under simple and stratified random sampling, PLoS One, 15 (2020), e0239098. https://doi.org/10.1371/journal.pone.0239098 doi: 10.1371/journal.pone.0239098
[6]	S. Ahmad, S. Hussain, M. Aamir, U. Yasmeen, J. Shabbir, Z. Ahmad, Dual use of auxiliary information for estimating the finite population mean under the stratified random sampling scheme, J. Math., 2021 (2021), 3860122. https://doi.org/10.1155/2021/3860122 doi: 10.1155/2021/3860122
[7]	N. Ali, I. Ahmad, M. Hanif, U. Shahzad, Robust-regression-type estimators for improving mean estimation of sensitive variables by using auxiliary information, Commun. Stat.-Theor. M., 50 (2021), 979–992. https://doi.org/10.1080/03610926.2019.1645857 doi: 10.1080/03610926.2019.1645857
[8]	J. Shabbir, S. Ahmed, A. Sanaullah, R. Onyango, Measuring performance of ratio-exponential-log type general class of estimators using two auxiliary variables, Math. Probl. Eng., 2021 (2021), 5245621. https://doi.org/10.1155/2021/5245621 doi: 10.1155/2021/5245621
[9]	U. Shahzad, M. Hanif, I. Sajjad, M. M. Anas, Quantile regression-ratio-type estimators for mean estimation under complete and partial auxiliary information, Sci. Iran., 29 (2022), 1705–1715. https://doi.org/10.24200/sci.2020.54423.3744 doi: 10.24200/sci.2020.54423.3744
[10]	A. Kumar, A. S. Siddiqui, Enhanced estimation of population mean using simple random sampling, Res. Stat., 2 (2024), 2335949. https://doi.org/10.1080/27684520.2024.2335949 doi: 10.1080/27684520.2024.2335949
[11]	A. Kumar, S. Bhushan, W. Emam, Y. Tashkandy, M. J. S. Khan, Novel logarithmic imputation procedures using multi auxiliary information under ranked set sampling, Sci. Rep., 14 (2024), 18027. https://doi.org/10.1038/s41598-024-68940-4 doi: 10.1038/s41598-024-68940-4
[12]	F. Smarandache, Neutrosophic set a generalization of the intuitionistic fuzzy set, Int. J. Pure Appl. Math., 24 (2005), 287.
[13]	Z. Tahir, H. Khan, M. Aslam, J. Shabbir, Mahmood, F. Smarandache, Neutrosophic ratio-type estimators for estimating the population mean, Complex Intell. Syst., 7 (2021), 2991–3001. https://doi.org/10.1007/s40747-021-00439-1 doi: 10.1007/s40747-021-00439-1
[14]	S. K. Yadav, F. Smarandache, Generalized neutrosophic sampling strategy for elevated estimation of population mean, Infinite Study, 2023.
[15]	V. K. Yadav, S. Prasad, Neutrosophic estimators in two-phase survey sampling, Neutrosophic Sets Sy., 61 (2023), 29. Available from: https://digitalrepository.unm.edu/nss_journal/vol61/iss1/29.
[16]	V. K. Yadav, S. Prasad, Neutrosophic estimators for estimating the population mean in survey sampling, Meas.-Interdiscip. Res., 22 (2024), 373–397. https://doi.org/10.1080/15366367.2023.2267835 doi: 10.1080/15366367.2023.2267835
[17]	M. A. Alqudah, M. Zayed, M. Subzar, S. A. Wani, Neutrosophic robust ratio type estimator for estimating finite population mean, Heliyon, 10 (2024), 1–12. https://doi.org/10.1016/j.heliyon.2024.e28934 doi: 10.1016/j.heliyon.2024.e28934
[18]	S. Masood, B. Ibrar, J. Shabbir, A. Shokri, Z. Movaheedi, Estimating neutrosophic finite median employing robust measures of the auxiliary variable, Sci. Rep., 14 (2024), 10255. https://doi.org/10.1038/s41598-024-60714-2 doi: 10.1038/s41598-024-60714-2
[19]	G. K. Vishwakarma, A. Singh, Generalized estimator for computation of population mean under neutrosophic ranked set technique: An application to solar energy data, J. Comput. Appl. Math., 41 (2022), 144. https://doi.org/10.1007/s40314-022-01820-7 doi: 10.1007/s40314-022-01820-7
[20]	R. Singh, A. Kumari, Neutrosophic ranked set sampling scheme for estimating population mean: An application to demographic data, Neutrosophic Sets Sy., 68 (2024), 246–270.
[21]	H. M. Samawi, H. A. Muttlak, Estimation of ratio using rank set sampling, Biometrical J., 38 (1996), 753–764. https://doi.org/10.1002/bimj.4710380616 doi: 10.1002/bimj.4710380616
[22]	P. L. H. Yu, K. Lam, Regression estimator in ranked set sampling, Biometrics, 53 (1997), 1070–1080. https://doi.org/10.2307/2533564 doi: 10.2307/2533564
[23]	S. Bhushan, A. Kumar, Log type estimators of population mean under ranked set sampling, predictive analytics using statistics and big data: Concepts and modeling, Bentham Science Publisher, 28 (2020), 47–74. https://doi.org/10.2174/9789811490491120010007
[24]	V. L. Mandowara, N. Mehta, Efficient generalized ratio-product type estimators for finite population mean with ranked set sampling, Aust. J. Stat., 42 (2013), 137–148. https://doi.org/10.17713/ajs.v42i3.147 doi: 10.17713/ajs.v42i3.147

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