Efficient Class of Neutrosophic Estimators of Population Mean under Uncertainty using Simple Random Sampling

In survey sampling, the traditional estimators frequently rely on the assumptions regarding the accuracy and certainty of the data, which may not always hold in practical applications, potentially leading to errors or missing information. In contrast, the neutrosophic estimators extend beyond the conventional binary framework of true-false by introducing a third component, ‘indeterminacy’. This additional component allows for a more comprehensive and flexible analysis that accounts for the imprecise, contradictory, and partially known nature of data. By explicitly incorporating uncertainty, the neutrosophic estimators provide a more robust alternative for real-world scenarios where data quality is uncertain. This study introduces an efficient class of neutrosophic estimators for estimating the population mean under uncertainty using simple random sampling (SRS). The proposed estimators are developed by integrating the neutrosophic framework into the traditional estimation techniques, enhancing their adaptability to uncertain and ambiguous data structures. Expressions for the bias and mean square error (MSE) of the proposed neutrosophic estimators are derived under the first-order approximation. To evaluate their relative performance, the mathematical conditions are established to compare the proposed neutrosophic estimators with the conventional ones. These theoretical findings are rigorously examined through an extensive simulation study that assesses the efficiency and robustness of the estimators across various data scenarios. Additionally, a real-data application further validates the practical utility of the proposed estimators, demonstrating their superiority in handling uncertainty compared to the traditional estimators. The findings highlight the potential of the neutrosophic estimation in improving the statistical inference by accommodating data imperfections, making it a valuable approach for real-world applications where the conventional assumptions may not hold.