Summary: M. Khoshnevisan et al. [A general family of estimators for estimating population mean using known value of some population parameter(s). Far East J. Theor. Stat. 22, No. 2, 181–191 (2007; Zbl 1133.62005)] introduced a family of estimators using auxiliary information in simple random sampling. They showed that these estimators are more efficient than the classical ratio estimator and that the minimum value of the mean square error (MSE) of this family is equal to the MSE of the regression estimator.
We propose another family of estimators using the results of B. Prasad [Some improved ratio type estimators of population mean and ratio in finite population sample surveys. Commun. Stat., Theory Methods 18, No. 1, 379–392 (1989; Zbl 0696.62012)]. Expressions for the bias and MSE of the proposed family are derived. Besides, considering the minimum cases of these MSE equations, a comparison of the efficiency conditions between the Khoshnevisan and the proposed family are obtained. The proposed family of estimators is found to be more efficient than Khoshnevisan’s family of estimators under certain conditions. Finally, these theoretical findings are illustrated by a numerical example with original data.