Title: Improvement in estimation of population variance utilising known auxiliary parameters for a decision-making model
Authors: Dinesh K. Sharma; S.K. Yadav; Hari Sharma
Addresses: Department of Business, Management and Accounting, University of Maryland Eastern Shore, Princess Anne, MD, USA ' Department of Statistics, Babasaheb Bhimrao Ambedkar University, Lucknow, India ' Department of Accounting and Finance, Virginia State University, VA, USA
Abstract: There is variation in similar things, whether natural or artificial. It is therefore in our best interest to estimate this variation. In this article, we suggest a Searls ratio type estimator for the main variable using the available information on the tri-mean and the third quartile of the auxiliary variable for an enhanced population variance estimation. The bias and mean squared error (MSE) of the proposed estimator are derived up to the first-degree approximation. The optimal value of the characterising scalar is obtained and, for this optimal value, the least MSE is achieved. The suggested estimator is compared with the competing estimators based on their MSEs, both theoretically and empirically. The calculation of biases and MSEs of suggested and competing estimators are accomplished by using R programming. The study's outcome is evidenced in the least MSE of the proposed model compared to competing estimators used in the study for business decision making.
Keywords: population variance; Searls type estimator; auxiliary variable; bias; mean squared error; MSE; percentage relative efficiency; PRE.
International Journal of Mathematical Modelling and Numerical Optimisation, 2022 Vol.12 No.1, pp.15 - 28
Received: 09 Sep 2020
Accepted: 17 Feb 2021
Published online: 20 Dec 2021 *