Neutrosophic exponential estimators for estimating the population mean using auxiliary attributes: An application to temperature data

Abstract

Classical statistical methods cannot directly incorporate measurement uncertainties and indeterministic elements into the model, leading to estimation errors and biases, especially in environmental datasets. Neutrosophic statistics, on the other hand, offers a broader approach that does not only rely on exact values, but also includes ambiguous, incomplete and conflicting information. In this study, we propose a new neutrosophic ratio-type estimator for estimating the population mean using monthly temperature data for Turkey for the period 2010-2022. This study proposes neutrosophic multivariate exponential estimators considering two auxiliary attributes. The mean square error equations of all proposed neutrosophic exponential estimators are obtained theoretically. Some conditions of neutrosophic multivariate exponential estimators are considered and the properties of these estimators are studied. The effectiveness of the proposed neutrosophic exponential estimators is analyzed using neutrosophic temperature data. In addition to real data analysis, extensive simulation studies are conducted under various scenarios to evaluate the performance of the estimators. The results demonstrate that the proposed estimators perform effectively under uncertainty and can be successfully applied in forecasting environmental variables.

Keywords

• Exponential estimator
• mean square error
• neutrosophic
• temperature

References

1. [1] R. E. Bellman and L. A. Zadeh, Decision-making in a fuzzy environment, Manag. Sci. 17(4), B–141, 1970.
2. [2] F. Smarandache, Neutrosophy: Neutrosophic Probability, Set, and Logic: Analytic Synthesis & Synthetic Analysis, 1998.
3. [3] F. Smarandache, Introduction to Neutrosophic Statistics, Sitech and Education Publisher, Craiova, Romania-Educational Publisher, Columbus, Ohio, USA, 2014.
4. [4] Z. Tahir, H. Khan, M. Aslam, J. Shabbir, Y. Mahmood and F. Smarandache, Neutrosophic ratio-type estimators for estimating the population mean, Complex Intell. Syst. 7(6), 2991– 3001, 2021.
5. [5] 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(2), 262–275, 1940.
6. [6] Z. Tahir, H. Khan, F. S. Alamri and M. Aslam, Neutrosophic ratio-type exponential estimators for estimation of population mean, J. Intell. Fuzzy Syst., (Preprint) 1–25, 2023.
7. [7] B. V. S. Sisodia and V. K. Dwivedi, Modified ratio estimator using coefficient of variation of auxiliary variable, J. Indian Soc. Agric. Stat. 1981.
8. [8] S. Bahl and R. Tuteja, Ratio and product type exponential estimators, J. Inf. Optim. Sci. 12(1), 159–164, 1991.

9. [9] L. N. Upadhyaya and H. P. Singh, Use of transformed auxiliary variable in estimating the finite population mean, Biom. J. 41(5), 627–636, 1999.
10. [10] C. Kadilar and H. Cingi, Improvement in estimating the population mean in simple random sampling, Appl. Math. Lett., 19(1), 75–79, 2006.
11. [11] H. P. Singh and R. Tailor, Estimation of finite population mean using known correlation coefficient between auxiliary characters, Statistica 65(4), 407–418, 2005.
12. [12] S. K. Yadav and F. Smarandache, Generalized neutrosophic sampling strategy for elevated estimation of population mean, Infinite Study, 2023.
13. [13] R. Singh and A. Kumari, Neutrosophic ranked set sampling scheme for estimating population mean: An application to demographic data, Neutros. Sets Syst. 68, 246–270, 2024.
14. [14] A. Ullah, J. Shabbir, A. M. Alomair and M. A. Alomair, Ratio-type estimator for estimating the neutrosophic population mean in simple random sampling under intuitionistic fuzzy cost function, Axioms 12(9), 890, 2023.
15. [15] M. A. Alqudah, M. Zayed, M. Subzar and S. A. Wani, Neutrosophic robust ratio type estimator for estimating finite population mean, Heliyon 10(8), 2024.
16. [16] T. Zaman, M. Sagir and M. ahin, A new exponential estimators for analysis of COVID19 risk, Concurr. Comput.: Pract. Exp. 34(10), e6806, 2022.
17. [17] Turkish State Meteorological Service, Monthly average temperature, monthly minimum temperature, monthly maximum temperature, Ankara: Turkish State Meteorological Service, 2024.