Development of improved estimators of finite population mean in simple random sampling with dual auxiliaries and its application to real world problems.

In general, the incorporation of supplementary information reduces the Mean Square Error (MSE) and, consequently, enhances the precision of estimating a population parameter. This improvement relies on the appropriate application of a suitable function, with careful consideration. This study introduces two innovative families of estimators for the finite population mean, both of which exhibit superior performance in scenarios involving dual auxiliary information in simple random sampling. Expressions up to the first-order approximation, for bias, and Mean Square Error were derived, and the conditions under which these proposed families surpassed the existing estimators. Our evaluation involved the use of both real and simulated data to compute the Mean Square Error and Percent Relative Efficiency (PRE) of the estimators. A comparative analysis revealed that under the specified conditions, both proposed families yielded more precise results.