Modified product estimator under two–phase sampling

Abstract

In this paper, modification of product estimator under two-phase sampling was suggested. The modified product estimator was obtained through transformation in two cases using sample mean of auxiliary variables. Case one was when the second sample was drawn from the first sample while case two was when the second sample was drawn from the population. The bias and mean square error (MSE) of the modified product estimator was obtained. The theoretical and numerical validity of the modified product estimator under the two cases were determined to show it superiority to some considered existing product estimators. Numerical results shows that the modified product estimator under the two cases were more efficient than the considered existing estimators.

Keywords: Product estimator, Two-Phase Sampling, Bias, Mean Square Error