Improved family of estimators for the population mean using supplementary variables under PPS sampling

In this article, we suggest an enhanced family of estimators for estimation of population mean employing the supplementary variables under probability proportional to size sampling. Up to the first order of approximation, numerical formulations of the bias and mean square error of estimators are obtained. From our suggested improved family of estimators, we give sixteen different members. The recommended family of estimators has specifically been used to derive the characteristics of sixteen estimators based on the known population parameters of the study as well as auxiliary variables. The performances of the suggested estimators have been assessed using three actual data. Furthermore, a simulation investigation is also accompanied to evaluate the effectiveness of estimators. The proposed estimators have a smaller MSE and an advanced PRE when linked to existing estimators, which are based on actual data sets and simulation studies. Theoretically and empirically studies also reveal that the suggested estimators accomplish well than the usual estimators.