Title: New modified ratio type estimator of the population mean using the known median of the study variable

Authors: S.K. Yadav; Dinesh K. Sharma; S.S. Mishra

Addresses: Department of Statistics, Babasaheb Bhimrao Ambedkar University, Lucknow-226025, U.P., India ' Department of Business, Management and Accounting, University of Maryland Eastern Shore, Princess Anne, MD 21853, USA ' Department of Mathematics and Statistics (Centre of Excellence on Advanced Computing), Dr. Ram Manohar Lohia Avadh University, Faizabad-224001, U.P., India

Abstract: In this paper, we propose an estimator that utilises the known value of the population median of the study variable under simple random sampling without replacement (SRSWOR). As per requirement and for comparison, we derived the bias and mean squared error (MSE) of the proposed estimator to the first degree of approximation. The optimum values of the characterising constants involved in the proposed estimator were also obtained. The characterising scalar may take different values which results in different values of MSE of proposed estimator; therefore its optimum value was obtained. The least value of MSE of proposed estimator is derived for this optimum value of characterising constant. Efficiency comparison of the proposed estimator has been made with other existing competing estimators of the population mean which makes use of auxiliary information under SRSWOR. Theoretical findings regarding the proposed estimator have been verified through the numerical study. It has been shown through a numerical example that the proposed estimator has the least MSE among other existing competing estimators of the population mean of the study variable.

Keywords: population median; auxiliary variable; bias; mean squared error; MSE; relative efficiency.

DOI: 10.1504/IJOR.2021.115625

International Journal of Operational Research, 2021 Vol.41 No.2, pp.151 - 167

Received: 25 Mar 2018
Accepted: 27 Jun 2018
Published online: 15 Jun 2021 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article