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Logarithmic Ratio and Product Estimators of Mean under Two-Phase Sampling

Sarbjit S. Brar, Jagmeet Singh Bajwa


In this paper, the logarithmic ratio and logarithmic product estimators of the mean are proposed under two-phase sampling. Approximate expressions of the biases and mean square errors of the same are obtained up to order . Under real-life situations, the proposed estimators are more efficient than the corresponding usual ratio and product type estimators. Further, under certain conditions, proposed estimators' biases are less than that of corresponding exponential ratio and product estimators'. The optimum sample sizes for the first and second phases which minimizes the proposed estimators' mean square errors are also obtained for a given cost. A simulation study using R software is conducted for real and hypothetical populations to demonstrate the theoretical results.

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