Handling Imprecise Climate Information: A Neutrosophic Generalized Estimator Under Stratified Ranked Set Sampling for Population Mean

Researchers under classical statistics often rely on precise, determinate data to estimate population parameters. However, in certain situations, data may be indeterminate or imprecise. Traditional approaches often fail to manage the complexities of uncertainty, necessitating the development of advanced methodologies like neutrosophic statistics. To address these challenges by handling vague, indeterminate, and uncertain information effectively, the study employed an entirely novel sampling technique known as “neutrosophic stratified ranked set sampling†and designed specialized neutrosophic estimators to enhance the accuracy of population mean estimation under uncertainty. This study developed neutrosophic generalized estimators that incorporate auxiliary information within the stratified ranked set sampling framework, leading to more precise population mean estimation under ambiguous conditions. Theoretical assessments included the derivation of bias and mean squared error (MSE) equations for these estimators, providing deeper insight into their efficiency. The performance of the proposed estimator was evaluated using simulated data using the R programming language as well as real-world datasets with indeterminate data, including relative humidity. The results demonstrated that the new estimators outperformed traditional methods in terms of MSE and percentage relative efficiency (PRE), highlighting their superior accuracy. By producing interval-based results, the proposed methodology provided a more comprehensive representation of uncertainty in population parameter estimation. This, along with reduced MSE, significantly improved the estimators’ reliability. The empirical validation, supported by numerical experiments and simulations conducted in R, further reinforces the practicality and robustness of the proposed methods, affirming their relevance for real-world applications.