Improved neutrosophic exponential-ratio estimator of population mean with simple random sampling

In this paper we present a neutrosophic exponential-ratio estimator for calculating the population mean using simple random sampling. In sampling methods classical statistics always depends on exact and complete data, but when we are dealing with unclear data these all become insufficient. By managing ambiguous and indeterminate data, neutrosophic statistics an extension of fuzzy and classical statistics addresses this drawback. The bias and mean square error (MSE) of proposed estimator are derived up to the first approximation order. Comparative study shows that it is more efficient than existing estimators, especially when we are working with data that is imprecise or of the neutrosophic kind. The proposed approach produces interval-based estimations in contrast to traditional estimators, which summarizes the unknown population mean with minimal MSE, improving reliability. The effectiveness of the estimator is confirmed by simulations and neutrosophic data sets, highlighting its potential in situations where uncertainty is common in the real world.