The problem of estimating the variance of a finite population is an important issue in practical situations where controlling variability is difficult. During experiments conducted in the fields of agriculture and biology, researchers often face this issue, resulting in outcomes that appear uncontrollable for the desired results. Using auxiliary information effectively has the potential to enhance the precision of estimators. This article aims to introduce improved classes of efficient estimators that are specifically designed to estimate the study variable's finite population variance. When stratified random sampling is used, these estimators are particularly efficient when the minimum and maximum values of the auxiliary variable are known. The bias and mean squared error (MSE) of the proposed classes of estimators are determined by a first-order approximation. In order to evaluate their performance and verify the theoretical results, we performed simulation research. The proposed estimators show higher percent relative efficiencies ($PREs$) in all simulation scenarios compared to other existing estimators, according to the results. Three datasets are utilized in the application section, which are used to further validate the effectiveness of the proposed estimators.

This article presents an improved class of efficient estimators aimed at estimating the finite population variance of the study variable. These estimators are especially useful when we have information about the minimum/maximum values of the auxiliary variable within a framework of simple random sampling. The characteristics of the proposed class of estimators, including bias and mean squared error ($MSE$) under simple random sampling are derived through a first-order approximation. To assess the performance and validate the theoretical outcomes, we conduct a simulation study. Results indicate that the proposed class of estimators has lower $MSEs$ as compared to other existing estimators across all simulation scenarios. Three datasets are used in the application section to emphasize the effectiveness of the proposed class of estimators over conventional unbiased variance estimators, ratio and regression estimators, and other existing estimators.

To estimate the finite population variance of the study variable, this paper proposes an improved class of efficient estimators using different transformations. When both the minimum and maximum values of the auxiliary variable are known and the ranks of the auxiliary variable are associated with the study variable, these estimators are particularly useful. Therefore, the precision of the estimators can be effectively improved through the utilization of these rankings. We examine the properties of the proposed class of estimators, including bias and mean squared error (MSE), using a first-order approximation through a stratified random sampling method. To determine the performances and validate the findings mathematically, a simulation study is carried out. Based on the results, the proposed class of estimators performs better in terms of the mean squared error $\left(MSE\right)$ and percent relative efficiency $\left(PRE\right)$ as compared to other estimators in all scenarios. Furthermore, in order to prove that the performances of the improved class of estimators are better than those of the existing estimators, three data sets are examined in the application section.

This article presents a new set of estimators designed to estimate the finite population variance of a study variable in two-phase sampling. These estimators utilize the information about extreme values and ranks of an auxiliary variable. Through a first-order approximation, we investigate the properties of these estimators, including biases and mean squared errors (MSEs). Furthermore, a comprehensive simulation study is conducted to assess their performance and validate our theoretical insights. Results demonstrate that our proposed class of estimators performs better in terms of percent relative efficiency (PRE) across various simulation scenarios compared to existing estimators. In addition, in the application section, we utilize three data sets to further validate the performance of our proposed estimators against conventional unbiased variance estimators, ratio and regression estimators, as well as other existing methods.

This article suggests an improved class of efficient estimators that use various transformations to estimate the finite population variance of the study variable. These estimators are particularly helpful in situations where we know about the minimum and maximum values of the auxiliary variable, and the ranks of the auxiliary variable are associated with the study variable. Consequently, these rankings can be applied as an effective tool to improve the accuracy of the estimator. A first-order approximation is used to investigate the properties of the proposed class of estimators, such as bias and mean squared error ($MSE$) under simple random sampling. A simulation study carried out in order to measure the performance and verify the theoretical results. The suggested class of estimators has a greater percent relative efficiency ($PRE$) than the other existing estimators in all of the simulated situations, according to the results. Three symmetric and asymmetric datasets are examined in the application section in order to show the superior performance of the proposed class of estimators over the existing estimators.

Outlier values and rankings are important for emphasizing data distribution variability, which improves the accuracy and effectiveness of variance estimations. To enhance the estimation of finite population variance in a two-phase sampling framework, this study presents an improved class of double exponential-type estimators by utilizing the outlier values and ranks of an auxiliary variable. A theoretical analysis is conducted to derive the biases and mean squared errors (MSEs) of these estimators using first-order approximations. A comprehensive simulation study is then performed to analyze the performance of the proposed estimators. The results clearly show that the new estimators provide more precise estimates, achieving a higher percentage relative efficiency (PRE) across all simulated scenarios. Furthermore, three data sets are analyzed to further confirm the efficiency of the proposed estimators as compared to other existing estimators. These results emphasize the potential of the proposed class of estimators to optimize variance estimation techniques, making it a more cost-effective and accurate choice for researchers using two-phase sampling in a variety of domains.