Estimation of Population Mean using Neutrosophic Exponential Estimators with Application to Real Data

One of the traditional problems in survey sampling is to estimate the population parameter like mean variance etc. This article investigates the mathematical derivations and application of neutrosophic statistics to address the challenges posed by imprecise, indeterminacies or ambiguous data, such as daily stock prices, weather forecast, social media sentiment and temperatures. The suggested estimators are highly useful for computing results while working with unclear, hazy, and neutrosophic-type data. These estimators produce answers that are interval-form rather than single-valued, which may give our population parameter a better chance of being off. We propose three novel neutrosophic exponential ratio-type estimators for the population mean, utilizing information of neutrosophic auxiliary variables. Expressions for bias and mean square error (MSE) of these estimators are derived using first-order approximations to assess their performance in terms of accuracy. To demonstrate their effectiveness, we apply the proposed estimators to real-life neutrosophic data sets. Additionally, a simulation study shows that our estimators outperform existing methods in terms of MSEs and percentage relative efficiency (PREs). This study further expands its originality by including pre-existing estimators into the neutrosophic framework, showcasing its versatility and adaptability. The results suggest that neutrosophic statistics provide a robust framework for analyzing uncertain data, facilitating more reliable decision-making in various applications.