Efficient Modified Estimator for the Mean Estimation Using Auxiliary Information in Sample Surveys

Several researchers use the auxiliary information to enhance the efficiency of their estimators in estimating the population parameters in sample surveys. Studies aim to find out more efficient estimators than recently proposed estimators and make inferences about the unknown population parameters such as population total, population mean, population proportion, or population variance. And one of the population parameters that are widely studied and used, is the population means. In this paper, the author attempts to develop a new modified estimator for the mean of the population in simple random sampling without replacement (SRSWOR) by utilizing information on four auxiliary variables. Therefore, the new estimators with their properties up to the first degree of approximation such as bias and Mean Squared Error (MSE) have been studied. In addition, the optimum value of the real numbers and the minimum MSE of the proposed estimators have been investigated. A few members were also derived from the proposed estimators by allocating the different suitable values of constants. Furthermore, the efficiency of the proposed estimators has been compared with other relevant existing estimators through theoretical study. While the data of peppermint oil production data in Digha India is used for the empirical study to compare the performance of the new estimator with other existing estimators.  The results of this paper showed that the new estimators are more efficient under the criteria of MSE and Percent Relative Efficiencies (PRE) as compared to all other consideration estimators for certain natural populations available in the literature.