Construction Of Almost Unbiased Estimator for Population Median Using Neutrosophic  Information

Rajesh Singh; Anamika Kumari; Florentin Smarandache; Sunil Kumar Yadav

Authors

Rajesh Singh Department of Statistics, Institute of Science, Banaras Hindu University, Varanasi-221005, Uttar Pradesh, India
Anamika Kumari Department of Data Science and Computing, DOE, Manipal Academy of Higher Education
Florentin Smarandache Department of Mathematics, University of New Mexico, 705 Gurley Ave, Gallup, USA
Sunil Kumar Yadav Department of Statistics, Institute of Science, Banaras Hindu University, Varanasi-221005, Uttar Pradesh, India

Keywords:

Neutrosophic auxiliary information, Population median, Almost unbiased estimators, Mean square error, Percent relative efficiency, Exponential estimator, Logarithmic estimator.

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.