New comprehensive mean estimation using regression-cum-exponential type estimator: Application with neutrosophic data

Abstract

When the point estimator is used to estimate population parameters, it provides a single value. In such a scenario, the neutrosophic method is beneficial for estimating the parameters of interest in sampling theory as it yields interval estimates where the parameter value mainly originates. Neutrosophic statistics focuses on uncertain or imprecise data. In this article, we suggest a new enhanced neutrosophic class of estimators to estimate the population mean. The properties (bias and mean squared error) are derived from the first-degree approximation. The suggested estimators are useful when working with uncertain, unclear, neutrosophic-type data. The best possible values of the defining scalars characterizing constants and the minimum neutrosophic mean squared error (MSE) for the suggested estimators are determined for these ideal values. Neutrosophic estimators outperform their classical counterparts because the existing estimated interval includes the minimum MSE when estimating the population mean. We use a simulation study and a real dataset from the Islamabad Stock Exchange. Variations in parameter and estimator combinations are reflected in the MSE values. From the numerical results, the estimators ${\widehat{\stackrel{‾}{Y}}}_{PN}$, ${\widehat{\stackrel{‾}{Y}}}_{SKN}$, and ${\widehat{\stackrel{‾}{Y}}}_{AN}$ have substantially higher MSE values, suggesting more significant estimation error. The estimators ${\widehat{\stackrel{═}{Y}}}_{GPi}$ (i = 1, 2, 3, 4, and 5) show better accuracy performance with relatively minimum MSE values. The numerical outcome shows that the suggested classes of estimators perform well as compared to the existing estimators.