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Improved Ratio and Product Type Estimators of Finite Population Mean in Two-phase Sampling

Gajendra K. Vishwakarma, Sayed Mohammed Zeeshan, Manish Kumar


In this paper, improved ratio and product type estimators have been developed for estimating the finite population mean of the study variable using auxiliary information in two-phase sampling. The expressions for the bias and mean square error (MSE) of the proposed estimators are obtained under first order of approximation. Theoretical and empirical studies have been done to demonstrate the efficiencies of the proposed estimators over other well known estimators.


Auxiliary variate, Study variate, Two-phase sampling, Bias, MSE.

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