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The proposed estimator of the population mean is based on a modification of the shape of the distribution of an auxiliary variable. If the theoretical correlation between the study and the auxiliary variables is less than a term that is proportional to the coefficient of variation of the auxiliary variable divided by the coefficient of variation of the study variable, then the modification of the distribution of the auxiliary variable reduces the bias and the mean square error of the estimator. A simulation confirms the analytical results. Application to air pollution data in Nan, Thailand, shows that on average, the biases of the estimators based on the modified auxiliary variable are reduced by 70% to 98% and the mean square errors by 91% to 100% compared to the estimators based on the unmodified auxiliary variable.

mathematical population studies

Bias and mean square error reduction by changing the shape of the distribution of an auxiliary variable: application to air pollution data in Nan, Thailand