A generalized Neutrosophic exponential product-type estimator under indeterminate data conditions

Authors

  • Anchal Yadav * Department of Statistics, University of Lucknow, Lucknow-226007, Uttar Pradesh, India.
  • Anuj Yadav Department of Mathematics, National Institute of Technology, Rourkela-769008, Odisha, India. https://orcid.org/0009-0005-5650-2549

https://doi.org/10.48313/uda.v3i2.89

Abstract

In classical statistical frameworks, estimating a population mean generally relies on exact observations along with auxiliary information. However, in many practical scenarios, such as financial markets and temperature measurements, data often appear imprecise, uncertain, or expressed in interval form. These characteristics reduce the efficiency and reliability of conventional estimation techniques. To address such challenges, neutrosophic statistics offer a more adaptable and comprehensive framework. This study introduces a neutrosophic exponential product–exponential type estimator aimed at estimating the finite population mean under uncertainty and indeterminacy, while minimizing the Mean Squared Error (MSE). Neutrosophic statistics extend traditional statistical methods by incorporating uncertainty, inconsistency, and incomplete information into the analysis. In this research, a neutrosophic exponential sine-type estimator is constructed by utilizing auxiliary information to estimate the neutrosophic mean of the study variable. The bias and MSE expressions of the proposed estimator are derived using first-order approximation methods. To assess performance, measures such as MSE and Percent Relative Efficiency (PRE) are employed. The results demonstrate that the proposed estimator outperforms several existing neutrosophic estimators. Furthermore, its practical relevance is validated using real-world datasets from medical sales and marketing sectors. Simulation studies are also conducted to verify the theoretical findings, confirming that the proposed estimator provides improved efficiency and reliability under uncertain conditions.  

Keywords:

Classical statistical techniques, Neutrosophic statistics theory, Exponential product-type estimator, Use of auxiliary information, Mean squared error, Percent relative efficiency

References

  1. [1] Cochran, W. G. (1940). The estimation of the yields of cereal experiments by sampling for the ratio of grain to total produce. The journal of agricultural science, 30(2), 262–275. https://doi.org/10.1017/S0021859600048012
  2. [2] Murthy, M. N. (1964). Product method of estimation. Sankhyā: The Indian journal of statistics, series a (1961-2002), 26(1), 69–74. http://www.jstor.org/stable/25049308
  3. [3] Sharma, P., Verma, H. K., Sanaullah, A., & Singh, R. (2013). Some exponential ratio-product type estimators using information on auxiliary attributes under second order approximation. International journal of statistics and economics, 12(3), 58–66. https://api.semanticscholar.org/CorpusID:96461978
  4. [4] Singh, R., & Sharma, P. (2015). A class of exponential ratio estimators of finite population mean using two auxiliary variables. Pakistan journal of statistics and operation research, 11(2), 221–229. https://doi.org/10.18187/pjsor.v11i2.759
  5. [5] Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8(3), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X
  6. [6] Smarandache, F. (2010). Neutrosophic logic-a generalization of the intuitionistic fuzzy logic. In Multispace & multistructure. Neutrosophic transdisciplinarity (100 collected papers of science) (Vol. 4, pp. 396). North-European Scientific Publishers, Hanko, Finland.
  7. [7] Smarandache, F. (2014). Introduction to neutrosophic statistics. Sitech & Education Publishing. https://books.google.com/books?id=3CLdBAAAQBAJ
  8. [8] Aslam, M. (2020). Monitoring the road traffic crashes using NEWMA chart and repetitive sampling. International journal of injury control and safety promotion, 28(1), 39–45. https://doi.org/10.1080/17457300.2020.1835990
  9. [9] Aslam, M. (2021). A new goodness of fit test in the presence of uncertain parameters. Complex & intelligent systems, 7(1), 359–365. https://doi.org/10.1007/s40747-020-00214-8
  10. [10] Smarandache, F. (2005). A unifying field in logics: Neutrosophic logic. Neutrosophy, neutrosophic set, neutrosophic probability (Fifth edition). American Research Press. https://doi.org/10.5281/zenodo.49174
  11. [11] Tahir, Z., Khan, H., Aslam, M., Shabbir, J., Mahmood, Y., & Smarandache, F. (2021). Neutrosophic ratio-type estimators for estimating the population mean. Complex & intelligent systems, 7(6), 2991–3001. https://doi.org/10.1007/s40747-021-00439-1
  12. [12] Singh, R., Kumari, A., Smarandache, F., & Tiwari, S. (2024). Construction of almost unbiased estimator for population mean using neutrosophic information. Neutrosophic systems with applications, 76, 449–463. https://doi.org/10.5281/zenodo.14010268
  13. [13] Yadav, S. K., & Smarandache, F. (2023). Generalized neutrosophic sampling strategy for elevated estimation of population mean. Neutrosophic sets & systems, 53, 221.
  14. [14] Vishwakarma, G. K., & Singh, A. (2022). Generalized estimator for computation of population mean under neutrosophic ranked set technique: An application to solar energy data. Computational and applied mathematics, 41(4), 144. https://doi.org/10.1007/s40314-022-01820-7
  15. [15] Kumar, S., Kour, S. P., Choudhary, M., & Sharma, V. (2022). Determination of population mean using neutrosophic, exponential-type estimator. Lobachevskii journal of mathematics, 43(11), 3359–3367. https://doi.org/10.1134/S1995080222140219
  16. [16] Alomair, A. M., & Shahzad, U. (2023). Neutrosophic mean estimation of sensitive and non-sensitive variables with robust hartley–ross-type estimators. Axioms, 12(6), 1–15. https://doi.org/10.3390/axioms12060578
  17. [17] Singh, A., Aslam, M., Vishwakarma, G. K., Dhital, A., & Patrascu, I. (2023). Neutrosophic regression cum ratio estimators for the population mean: An application in medical science. In Cognitive intelligence with neutrosophic statistics in bioinformatics (pp. 313–333). Academic Press. https://doi.org/10.1016/B978-0-323-99456-9.00018-0
  18. [18] Singh, R., & Kumari, A. (2024). Neutrosophic ranked set sampling scheme for estimating population mean: An application to demographic data. Neutrosophic sets and systems, 68, 246–270.
  19. [19] Singh, A., Kulkarni, H., Smarandache, F., & Vishwakarma, G. K. (2024). Computation of separate ratio and regression estimator under neutrosophic stratified sampling: An application to climate data. Journal of fuzzy extension and applications, 5(4), 605–621. https://digitalrepository.unm.edu/math_fsp/696/
  20. [20] Singh, P., & Gupta, S. (2024). Combining two auxiliary variables for elevated estimation of finite population mean under neutrosophic framework. Neutrosophic sets and systems, 76(1), 275–287. https://digitalrepository.unm.edu/nss_journal/vol76/iss1/16/
  21. [21] Singh, B., Singh, A., & Smarandache, F. (2025). A family of neutrosophic estimators for estimating mean: An application to real data. Sankhya b, 87(2), 712–741. https://doi.org/10.1007/s13571-025-00369-9
  22. [22] Yadav, S. K., Singh, R., & Tiwari, S. N. (2025). Estimation of population mean utilizing two neutrosophic Auxiliary variables with imprecise information. Uncertainty discourse and applications, 2(1), 17–31. https://doi.org/10.48313/uda.v2i1.51
  23. [23] Singh, R., & Tiwari, S. N. (2025). Improved estimator for population mean utilizing known medians of two auxiliary variables under neutrosophic framework. Neutrosophic systems with applications, 25(1), 38–52.
  24. [24] Yadav, V. K., & Prasad, S. (2024). Neutrosophic estimators for estimating the population mean in survey sampling. Measurement: Interdisciplinary research and perspectives, 22(4), 373–397. https://doi.org/10.1080/15366367.2023.2267835
  25. [25] Bahl, S., & Tuteja, R. K. (1991). Ratio and product type exponential estimators. Journal of information and optimization sciences, 12(1), 159–164. https://doi.org/10.1080/02522667.1991.10699058
  26. [26] Jerajuddin, M., & Kishun, J. (2016). Modified ratio estimators for population mean using size of the sample, selected from population. International journal of scientific research in science, engineering and technology, 2(2), 10–16. https://ijsrset.com/IJSRSET16221
  27. [27] Singh, R., Chauhan, P., Smarandache, F., & Sawan, N. (2007). Auxiliary information and a priori values in construction of improved estimators. Renaissance High Press. https://books.google.com/books?id=fhLeBAAAQBAJ
  28. [28] Gulzar, M. A., Abid, M., Nazir, H. Z., Zahid, F. M., & Riaz, M. (2020). On enhanced estimation of population variance using unconventional measures of an auxiliary variable. Journal of statistical computation and simulation, 90(12), 2180–2197. https://doi.org/10.1080/00949655.2020.1767620
  29. [29] Solanki, R. S., Singh, H. P., & Rathour, A. (2012). An alternative estimator for estimating the finite population mean using auxiliary information in sample surveys. International scholarly research notices, 2012(1), 657682. https://doi.org/10.5402/2012/657682
  30. [30] Raghav, Y. S. (2023). Neutrosophic generalized exponential robust ratio type estimators. International journal of analysis and applications, 21, 41. https://doi.org/10.28924/2291-8639-21-2023-41
  31. [31] Singh, P., Sharma, P., & Singh, A. (2025). Estimation of population mean using generalized neutrosophic exponential estimators. Research in mathematics, 12(1), 2474774. https://doi.org/10.1080/27684830.2025.2474774

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Published

2026-06-15

Issue

Vol. 3 No. 2 (2026): Uncertainty Discourse and Applications

Section

Articles

How to Cite

Yadav, A., & Yadav, A. . (2026). A generalized Neutrosophic exponential product-type estimator under indeterminate data conditions. Uncertainty Discourse and Applications, 3(2), 152-167. https://doi.org/10.48313/uda.v3i2.89

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