Logarithmic Ratio-Type Estimator for Finite Population Mean under Neutrosophic Framework

In the classical statistical framework, a precise and determinate dataset is used to estimate the population mean when auxiliary variables are known. In cases where the data is unclear or expressed in ranges, such as with daily city temperatures or stock prices, classical statistics fail to perform well in such situations. In these cases, neutrosophic statistics provide significantly greater precision. The primary objective of this study is to propose a neutrosophic estimator that minimizes the mean squared error (MSE) in estimating unknown finite population mean, particularly in cases where classical statistics fall short due to data ambiguity and indeterminacy. The concept of neutrosophic statistics was pioneered by Florentin Smarandache. It is a generalization of classical statistics that addresses ambiguous, unclear, vague, and indeterminate data. In this study, we present a neutrosophic logarithmic ratio-type estimator that uses known auxiliary information to estimate the neutrosophic mean of a study variable. The proposed estimators’ bias and MSE are analyzed through a first-order approximation. Based on the MSE and percent relative efficiency (PRE) criteria, the proposed estimator shows improved performance over existing neutrosophic estimators. The proposed estimator’s performance is validated through empirical studies, with its practical relevance demonstrated using real-life neutrosophic datasets from medical product sales and marketing. In addition, a simulation study was also carried out, showing that our proposed estimator performs better than those discussed in the previous studies.