Abstract
A modified efficient difference-type estimator for population mean under two-phase sampling design
Highlights
A uxiliary information is used either in the estimation stage or in the formation of an estimator to get improved designs and increase the efficiency of estimators in sampling technique
In [1], Laplace started the use of the auxiliary information in formulating ratio type estimation
The statisticians paid a lot of care towards the formation of new and efficient estimators for the population parameters estimation [2– 13]
Summary
A uxiliary information is used either in the estimation stage or in the formation of an estimator to get improved designs and increase the efficiency of estimators in sampling technique. Khan and Al-Hossain [14] suggested a generalized chain ratio in regression estimator for mean of the population using two auxiliary variables. A modified form of difference-type estimator for mean of the population using two-phase sampling is suggested [15]. Let x and y be the auxiliary and the study variables with corresponding values xi and yi respectively for the ith unit i = {1, 2, 3, . X = (1/N) ∑ xi i of the study as well as auxiliary variable respectively. ∑(xi − x) n−1 i be the corresponding sample variances of the study as well as auxiliary variable respectively. Cy = Sy , Cx = Sx and Cz = Sz. Z are the coefficient of variations of the study and the auxiliary variables respectively
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