Yadav, Akhilesh; Yadav, Dharmendra Kumar; Yadav, Subhash Kumar; Zaman, Tolga

Estimating the population mean using auxiliary information has been extensively explored within the classical framework. While point estimators offer simplicity, they provide only a single value without reflecting the uncertainty or variability inherent in real-world data. This shortcoming is particularly critical in high-precision applications and decision-making contexts. Moreover, classical estimators are often vulnerable to the influence of outliers, which can distort results and introduce significant bias. To address these limitations, this study introduces a novel estimator grounded in neutrosophic theory, which is specifically designed to handle imprecise, vague, and incomplete information-conditions frequently encountered in practical sampling scenarios. The proposed neutrosophic estimator incorporates auxiliary information expressed in neutrosophic terms, offering a more flexible and resilient estimation strategy. We derive expressions for the bias and mean square error of the proposed estimator under a first-order approximation. A comprehensive theoretical analysis, supported by simulation studies, confirms that the neutrosophic estimator consistently outperforms classical estimators in terms of accuracy and robustness, especially in uncertain environments. These findings underscore the potential of neutrosophic approaches as powerful alternatives to conventional estimation techniques in modern statistical inference.

Kumar, Surendra; Bari, Tarushree; Yadav, Subhash Kumar; Zaman, Tolga

This study presents an efficient method for estimating the population mean of a study variable using a Searls exponential ratio estimator. The approach is based on simple random sampling and leverages known population parameters of an auxiliary variable for enhanced estimation of population mean. Using large sample approximations up to the first order, the expressions for the bias and mean squared error of the proposed estimator are derived. To evaluate its performance, the estimator is compared conceptually and mathematically with several existing estimators. Theoretical results are further validated through both simulated and real-world data sets. Findings from these evaluations demonstrate that the proposed estimator consistently outperforms many competing estimators, particularly at higher population mean values. Therefore, it holds promise for improving population mean estimation across a range of practical applications.

Yadav, Subhash Kumar; Arya, Diksha; Sharma, Prayas; Zaman, Tolga

The Quest for the improved estimators of population mean is a continuous process to estimate it more efficiently and more closely to the true population mean of the study variable. There are various estimators of population mean in the literature, which estimate it efficiently, but still there is space for more efficient estimators. For improved estimation of population mean of primary variable, we suggest six different searls type ratio estimators utilizing the known auxiliary parameters. We derive the expressions for the biases and the mean squared errors of the introduced estimators for an approximation of degree one. The optimal values of the Searls characterizing constants, which minimize the mean squared errors of the introduced estimators, are obtained. The least value of the mean squared error of the proposed estimators for these optimal values of the characterizing scalars is also acquired. The efficiency of the proposed estimators is compared theoretically with the competing estimators of population mean through their mean squared errors. We derive the efficiency conditions of the proposed estimator for which it is more efficient than the estimators of population mean in competition. These efficiency conditions of the proposed estimators are verified through empirical data and the improvement over the competing estimators is calculated based on the minimum values of the mean squared errors. It is evident from the numerical study that the proposed estimator has the least mean squared error and the highest percentage relative efficiency in comparison to competing estimators. Thus, the proposed estimators are recommended for applications in different areas of applications.

Yadav, Subhash Kumar; Arya, Diksha; Koc, Tuba; Zaman, Tolga

The study provides an enhanced estimation of the population mean using known information on an auxiliary variable. An enhanced class of estimators is suggested for the same. The proposed estimator's bias and mean squared error (MSE) are calculated up to the first order of approximation. The optimum values of the characterizing constants are obtained by minimizing the MSE of the proposed estimator. The minimum MSE and the bias values are achieved by optimising the characterizing scalar. The MSE of the proposed estimator has also been compared both conceptually and empirically with the MSEs of competing estimators. Real and simulated data sets are adopted to verify the theoretical prerequisites for the proposed estimator's greater efficiency over competing estimators. The most efficient estimator is recommended for practical utility in different areas of applications and the suggested estimator filfills the requirement.