The efficiencies of the ratio-type estimators have been increased by using linear transformation on auxiliary variable in the literature. But such type of estimators requires the additional knowledge of unknown population parameters, which restricts their applicability. Keeping in view such restrictions, we have proposed two unbiased estimators of population mean of study variable on applying linear transformation to auxiliary variable by using its extreme values in the population that are generally available in practice. The comparison of the proposed estimators with the existing ones have been done with respect to their variances. It has also been shown that the proposed estimators have greater applicability and are more efficient than the mean per unit estimator even when the existing estimators are less efficient. We have also shown that under some known conditions the choice of most efficient estimators among the considered ones can be made for a given population. The theoretical results obtained are shown diagrammatically and have been verified numerically by taking some empirical populations.
Shabbir and Gupta (2007) introduced an exponential ratio-type estimator for the population variance and compare its mean square error with mean square error of some of the existing estimators. But unfortunately, the expression of mean square error of their proposed estimator is incorrect and hence the comparison based on incorrect mean square error, carried by them, is wrong. In the present article, the author provides the correct expression of the mean square error, up to first order of approximation, of the same estimator. A comparison has been made by taking the corrected expression of mean square error. The corresponding exponential ratiotype estimator for the population variance, under double sampling technique, is also proposed which followed by a comparison.
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