title: A note on a difference-type estimator for population mean under two-phase sampling design.
abstract: In this manuscript, we have proposed a difference-type estimator for population mean under two-phase sampling scheme using two auxiliary variables. The properties and the mean square error of the proposed estimator are derived up to first order of approximation; we have also found some efficiency comparison conditions for the proposed estimator in comparison with the other existing estimators under which the proposed estimator performed better than the other relevant existing estimators. We show that the proposed estimator is more efficient than other available estimators under the two phase sampling scheme for this one example; however, further study is needed to establish the superiority of the proposed estimator for other populations.
authors.affiliation: Department of Mathematics, COMSATS Institute of Information Technology, Abbottabad, 22060 Pakistan.
authors.forename: Mursala
authors.initials: M
authors.lastname: Khan
authors.affiliation: Department of Mathematics, Faculty of Science, Jazan University, Jazan, 2097 Saudi Arabia.
authors.forename: Abdullah Yahia
authors.initials: AY
authors.lastname: Al-Hossain
keywords: Auxiliary variable; Bias; Efficiency; Exponential chain-type estimator; Mean squared-error; Study variable; Two phase sampling