On the Efficiency of the Regression-Cum-Exponential Type Neutrosophic Estimators of Population Median in the Presence of Auxiliary Information
Magdalene Dooyum Gongul
Ahmed Audu
Dauran N.S.
Abdulhakeem Abdulazeez
Abstract
Estimation of population median accurately is often challenging when data are vague, imprecise, or indeterminate. Classical estimators which rely on precise data, may produce biased and inefficient results under such conditions. neutrosophic estimators have been developed to address the issues of vagueness, impreciseness, or indeterminateness on median estimation. However, some recent efficient existing median estimators depend on unknown constants which makes them impracticable in real life situations unless if the unknown parameters are estimated using a sample which require huge resources. These existing median estimators are also ratio-based which are less efficient when the correlation between the study variable and auxiliary variable is negative. To address these problems, this study introduced regression-cum-exponential-type neutrosophic estimators for the population median which are efficient and free of unknown constants. The proposed median estimators are regression-base estimators which are efficient for both negative and positive correlation. Theoretical expressions for biases and mean squared errors (MSEs) of the proposed neutrosophic median estimators were derived up to the first order of approximation and the theoretical efficiency conditions over the related existing estimators were established. The performances of the proposed estimators were evaluated empirically using biases, MSEs and percent relative efficiency (PRE) through simulation studies. The results indicate that the proposed estimators consistently outperform classical and existing methods by achieving lower MSE and higher PRE with exception of few cases. The findings highlight the accuracy, efficiency, and practical applicability of the proposed neutrosophic approach for median estimation in uncertain environments.
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