Constructing a new estimator for estimating population mean utilizing auxiliary information in probability proportional to size sampling

In some instances, the size of the target population might exhibit significant variation. In the medical investigation, the number of individuals troubled with a certain infection and the scale of the medical facilities may differ. Probability proportional to size (PPS) sampling helps to collect data in household income surveys when the number of siblings in houses fluctuates. This work aims to develop an improved estimator for estimating finite population mean using auxiliary information under PPS sampling. Utilizing the Taylor series approach, a novel and enhanced estimator is introduced to determine the expression of the mean square error up to the first degree of approximation. This estimator performs better as compared to some current existing estimators using theoretical efficiency constraints. The performance of the existing and newly designed estimators was evaluated by analyzing two actual data sets. The performance was assessed based on maximizing the percentage relative efficiency and minimizing the marginal mean square error. Compared to other estimator which is examined in this work, we found that the proposed technique exhibited superior performance and increased efficiency.