In this research, a logarithmic-type estimator was formulated for estimating the finite population variance in stratified random sampling. By ensuring that the sampling process is symmetrically conducted across the population, biases can be minimized, and the sample is more likely to be representative of the population as a whole. We conducted a comprehensive numerical study and simulation study to evaluate the performance of the proposed estimator. The mean squared error values were computed for both our proposed estimator and several existing ones, including the standard unbiased variance estimator, difference-type estimator, and other considered estimators. The results of the numerical study and simulation study demonstrated that the proposed log-type estimator outperforms the other considered estimators in terms of MSE and percentage relative efficiency. Graphical representations of the results are also provided to illustrate the efficiency of the proposed estimator. Based on the findings of this study, we conclude that the proposed log-type estimator is a valuable addition to the existing literature on variance estimation in stratified random sampling. It provides a more efficient and accurate estimate of the population variance, which can be beneficial for various statistical applications.

This pioneering investigation introduces two innovative estimators crafted to evaluate the finite population distribution function of a study variable, employing auxiliary variables within the framework of stratified random sampling and post-stratification while emphasizing symmetry in the sampling process. The derivation of mathematical expressions for bias and the mean square error up to the first degree of approximation fortifies the credibility of the proposed estimators. Drawing from three distinct datasets, including real-world data capturing student behaviors and exam performances from 500 students, this research highlights the superior efficiency of the proposed estimators compared to existing methods across both sampling schemes. Employing the proposed estimator, we effectively forecast students’ exam scores based on their study hours, backed by empirical evidence showcasing its precision in terms of mean square error and percentage relative efficiency. This study not only introduces inventive solutions to enduring challenges in survey sampling but also provides practical insights into enhancing predictive accuracy in educational assessments.

There is a difficulty in survey sampling when non-response (NR) occurs in the process of estimating the population parameters. This study examines the effectiveness of combined and separate log-type estimators when using bivariate auxiliary information when NR occurs in data. In this study, we propose families of novel log-type estimators under various scenarios. We performed an analysis on the reliability and efficiency of our proposed estimators in situations when NR occurs in both study and auxiliary variables and when NR occurs only in study variables. In this study, we have concentrated on certain issues like how the non-response effects the estimators’ efficiency, how different NR rates effect the precision of estimators, and how the combined and separate types of estimators handle the problem of NR. We proved the efficiency of our proposed estimators by using the bias and mean square error (MSE) metrics under different NR rates, illustrating the positive correlation between higher NR rates and increased errors. To evaluate the impact of NR on MSE values, we took four real datasets, which included a cost of living index dataset for 121 nations and another dataset which is essential for forecasting solar UV radiation hazards influenced by environmental factors, thus enhancing public health awareness and preventive strategies. Additionally, a simulation study comprising 10,000 iterations was also performed. This study provides survey practitioners with valuable guidance on selecting strong estimation methods to enhance the accuracy and efficiency of survey estimates in the context of non-response. This investigation contributes to the domain of survey sampling by demonstrating the robustness and effectiveness of log-type estimators. These estimators enhance survey findings by effectively addressing NR issues.

This comprehensive review delves into the landscape of estimators used in stratified sampling and post-stratification to estimate crucial population parameters, such as mean, median, variance, proportion, and distribution function. This study extensively examines the utilization of single and double auxiliary information, calibration weights, and various classes of estimators in the context of survey sampling, shedding light on their strengths and limitations. While these methods contribute significantly to enhancing estimation accuracy within stratified populations, this Review underscores challenges such as the dependence on accurate auxiliary information for single and double auxiliary methods, the assumption of ignorable nonresponse in calibration weights, and the need for careful consideration of underlying assumptions in a class of estimators. Future work in this field should focus on refining and validating these methodologies, addressing potential biases, and exploring innovative ways to handle nonresponses. Rigorous sensitivity analyses and investigations into the robustness of these techniques under varying conditions will be essential for advancing the precision and reliability of parameter estimation in the complex landscape of stratified sampling and post-stratification. This Review serves as a foundational resource for researchers and practitioners engaged in advancing the field and navigating the nuances of precise parameter estimation in survey sampling.

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