Computation of Improved Searls Estimation of Population Variance Using Robust Auxiliary Parameters

Variation is an inherent phenomenon, whether in natural things or man-made. Thus, it seems essential to estimate this variation. Various authors have worked in the direction of improved estimation of population variance utilizing the known auxiliary parameters for better policymaking. Methods: In this article, a new Searls ratio type class of estimator is suggested for elevated estimation of population variance of the main variable. As the suggested estimator is biased, its bias and mean squared error (MSE) has been derived up to the order-one approximation. The optimum values for the Searls characterizing scalars are obtained. The minimum MSE of the introduced estimator is obtained for the optimum Searls characterizing scalars. A theoretical comparison between the suggested estimator and the competing estimators has been made through their mean squared errors. The efficiency conditions of the suggested estimator over competing estimators are also obtained. These theoretical conditions are verified using some natural data sets. The computation of R codes for the biases and MSEs of the suggested and competing estimators is developed and used for three natural populations in the study by Naz et al. The estimator with the least MSE is recommended for practical utility. The empirical study has been done using R programming. Results: The MSEs of different competing and the suggested estimators are obtained for three natural populations. The estimator under comparison with the least MSE is recommended for practical applications. Discussion: The aim to search for the most efficient estimator for improved estimation is fulfilled through the proper use of the auxiliary parameters obtained from the known auxiliary variable. The suggested estimator may be used for elevated estimation of the population variance. Conclusion: The introduced estimator has the least MSE as compared to competing estimators of population variance for all three natural populations. Thus, it may be recommended for application in various fields.