Construction Of Almost Unbiased Estimator for Population Median Using Neutrosophic Information

Abstract

This paper introduces the development of an almost unbiased estimator for estimating the unknown population median of the primary variable. The proposed estimator leverages neutrosophic auxiliary information and employs simple random sampling without replacement (SRSWOR). In order to establish the efficacy of the proposed method, we derive the mathematical formulations for the mean square error (MSE), bias, and the minimum MSE of the estimator, providing approximations up to the first order. These derivations allow for a comprehensive analysis of the estimator's performance and its suitability for accurate population median estimation. To validate the theoretical results, we conduct an empirical study using two real-world datasets, ensuring that the proposed estimator's behavior aligns with theoretical predictions in practical scenarios. The study shows that the proposed estimator remains nearly unbiased, with minimal bias when approximated to the first order. This result further demonstrates that the estimator performs robustly across various data conditions. In comparison to existing estimators, the proposed estimator outperforms the others in terms of efficiency, as evidenced by the MSE and PRE values derived. The proposed method not only minimizes bias but also provides more accurate population median estimates with reduced estimation error, making it a more reliable tool in the context of uncertain or incomplete data, where traditional estimators might fall short. By bridging the gap between classical estimation techniques and modern methods that account for uncertainty, the proposed estimator offers a significant advancement in the field of statistical estimation, particularly in real-world applications involving uncertain datasets. The findings presented in this study contribute to the growing body of knowledge in statistical estimation, particularly in the use of neutrosophic information for enhancing estimator accuracy. Furthermore, the results provide a valuable foundation for future research aimed at developing more efficient and reliable statistical estimators for a variety of practical applications. © 2025, University of New Mexico. All rights reserved.