Abstract
Abstract
In traditional statistics, the population mean is estimated using exact and well-defined data whenever auxiliary information is present. Still, the resulting estimates commonly suffer from bias. The goal of this research is to formulate a neutrosophic estimator that yields a lower Mean Squared Error (MSE) for the unknown population mean and addresses the shortcomings of classical statistical methods when confronted with ambiguous data. The concept of neutrosophic statistics was introduced by Smarandache (Smarandache 2014), as an extension of classical statistics to address uncertainty, vagueness, and indeterminacy of data. This research constructs an almost unbiased neutrosophic estimator that incorporates known neutrosophic auxiliary information for estimating the study variable’s population mean. To assess the proposed estimator’s efficiency, its bias, MSE, and minimum MSE are mathematical derived under first-order approximations. Through these derivations, we can assess how effective the estimator is and how well it performs in estimating the population mean. The research confirms that the suggested estimator is almost unbiased, because its first-order bias is extremely small. The suggested estimator provides superior performance over traditional estimators in terms of both MSE and Percentage Relative Efficiency (PRE). For practical applications, priority should be given to the estimator that yields the highest PRE or exhibits the least MSE. The conclusions drawn theoretically are confirmed by an empirical study based on real datasets. Additionally, a simulation study was carried out, demonstrating that the estimator we proposed yields superior results compared to those already existing.