Modified Regression-Cum-Exponential Type Neutrosophic Estimators of Population Mean in the Presence of Auxiliary Information
Mabruka Adamu Gurori
Ahmed Audu
Zoramawa A. B.
Abdulhakeem Abdulazeez
Abstract
Neutrosophic statistics is a generalization of classical statistics and fuzzy logic that addresses ambiguous, imprecise, vague and indeterminate data. The concept of Neutrosophic statistics has been introduced in the development of estimators of population mean. The concept has extended to the development with estimators with two auxiliary variables. Some of the existing estimators of population mean with two auxiliary variables are functions of unknown parameters of auxiliary variables which makes them impracticable in real life situations. These existing estimators are either ratio-based, product-based or ratio-product-based which are less efficient when the correlation between the study and auxiliary variable is strong and negative. Therefore, to address the problem this study intends to proposed new classes of population mean estimators which are efficient and independent of unknown parameters. The proposed estimators are regression-based estimators which are applicable for either positive or negatives, weak or strong correlation. The properties (Biases and MSEs) of the proposed estimators are derived up to the first order of approximation. The theoretical efficiency conditions of the proposed estimators over some existing related estimators were established. The theoretical conclusions are validated by the empirical analysis, which made use of the simulated data. Empirical studies were conducted to assess the performances (Biases, MSEs and PREs) of the proposed estimator relative to existing estimators. The result revealed that the proposed estimators have minimum biases, minimum MSEs and higher PREs with exception of few cases compared to that of existing competing estimators considered in the study. These results demonstrate the superiority of the proposed estimator over the existing estimators in terms of the accuracy, efficiency and efficiency gain in the estimation of the population mean under Neutrosophic settings.
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