GENERALISED EXPONENTIAL RATIO-CUM-PRODUCT ESTIMATOR FOR ESTIMATING POPULATION VARIANCE IN SIMPLE RANDOM SAMPLING
Creators: name: Jan, Rafia
name: T.R. Jan
name: Faizan Danish
Publisher: name: Reliability: Theory & Applications
Year: 2023
Subjects: Exponential estimator
Auxiliary variable
Mean Square Error and Percent Relative Efficiency

description: This study presents a comprehensive investigation into the estimation of population variance for a study variable using Simple Random Sampling, with the incorporation of two auxiliary variables. To address the challenges of variance estimation in complex scenarios, a novel approach termed the "Proposed Generalized Exponential Ratio-cum-Product Estimator" is introduced. This innovative estimator belongs to a class of estimators that rely on exponential functions of the auxiliary variables, providing enhanced precision and efficiency in variance estimation. To thoroughly assess the performance of the proposed estimators, the research develops equations for both Mean Square Errors and Biases, unveiling their statistical properties. The study systematically explores the conditions under which these estimators demonstrate superior efficiency compared to traditional alternative estimators, thereby enabling researchers to identify contexts where their utilization is most beneficial. The empirical aspect of the research constitutes a significant contribution to the study's validity. Through empirical analysis, the proposed estimators are directly compared against the conventional Unbiased Sample Variance Estimator, showcasing their clear superiority in terms of efficiency. Furthermore, Mean Square Errors and Percent Relative Efficiency are calculated for all estimators and subjected to theoretical and empirical comparisons with existing estimation methods. These findings corroborate the advantageous attributes of the proposed estimator in real-world scenarios, reinforcing its practicality and reliability in various research domains. Beyond methodological developments, this study also delves into the real-world implications and applications of the proposed estimators. It highlights the potential benefits of utilizing these estimators in situations where study variables exhibit intricate relationships with auxiliary variables, offering valuable insights into multifaceted data sets and multidimensional factors. Additionally, a comprehensive sensitivity analysis is undertaken to assess the robustness of the proposed estimators under varying assumptions and sampling schemes. The researchers' meticulous evaluation enhances the credibility of the proposed estimators and ensures their adaptability across diverse practical scenarios. Overall, this study's significance extends beyond statistical theory, presenting valuable practical implications for researchers and practitioners across different fields. Improved population variance estimation leads to enhanced decision-making, optimal resource allocation, and deeper insights into underlying phenomena. By introducing the proposed estimator and thoroughly examining its performance through rigorous theoretical and empirical analyses, this research lays a solid foundation for more robust and efficient variance estimation techniques. The insights gained from this study can reshape statistical practices, paving the way for advancements in diverse scientific disciplines and inspiring further knowledge exploration.