A generalized Neutrosophic exponential product-type estimator under indeterminate data conditions

Abstract

In classical statistical frameworks, estimating a population mean generally relies on exact observations along with auxiliary information. However, in many practical scenarios, such as financial markets and temperature measurements, data often appear imprecise, uncertain, or expressed in interval form. These characteristics reduce the efficiency and reliability of conventional estimation techniques. To address such challenges, neutrosophic statistics offer a more adaptable and comprehensive framework. This study introduces a neutrosophic exponential product–exponential type estimator aimed at estimating the finite population mean under uncertainty and indeterminacy, while minimizing the Mean Squared Error (MSE). Neutrosophic statistics extend traditional statistical methods by incorporating uncertainty, inconsistency, and incomplete information into the analysis. In this research, a neutrosophic exponential sine-type estimator is constructed by utilizing auxiliary information to estimate the neutrosophic mean of the study variable. The bias and MSE expressions of the proposed estimator are derived using first-order approximation methods. To assess performance, measures such as MSE and Percent Relative Efficiency (PRE) are employed. The results demonstrate that the proposed estimator outperforms several existing neutrosophic estimators. Furthermore, its practical relevance is validated using real-world datasets from medical sales and marketing sectors. Simulation studies are also conducted to verify the theoretical findings, confirming that the proposed estimator provides improved efficiency and reliability under uncertain conditions.