Neutrosophic median estimation under uncertainty with empirical application to stock prices

In this study, neutrosophic statistics (NS) is explored as an advanced extension of both classical and fuzzy statistics aimed at addressing data uncertainty more effectively. This study introduces a new generalized class of estimators for estimating the finite population median (Md) under simple random sampling without replacement (SRSWOR), employing robust auxiliary information. The estimators discussed in this work provide an effective tool for dealing with vague, uncertain, and indeterminate information in NS analysis. In contrast to classical approaches that offer a single-point outcome, our estimators generate ranges that indicate the likely location of the population parameter. Furthermore, we outline the bias and mean squared error (MSE) of the proposed generalized estimator within the framework of a first-order approximation, demonstrating its better performance compared to the other estimators considered. The empirical study and simulation study demonstrated the practicality and efficacy of the suggested estimators in addressing imprecise or indeterminate data using stock price datasets. We further compare the recommended estimators to the existing ones using MSE and percentage relative efficiency (PRE). It is evident from the numerical results from empirical study and simulation study that our suggested estimator is more effective than the existing ones, with higher PRE and lower MSE. The empirical analysis confirms the theoretical conclusions, emphasizing the superiority of the proposed approach.