In some conditions, the size of the target population can vary considerably in their sizes. As an illustration, the size of health facilities and the number of sick person with a definite sickness can differ in a medical study. Also in the survey about household income, the number of siblings in a home can differ; for such condition the probability proportional to size sampling (PPS) provides effective results. In this article our goals is to suggest an improved class of estimators for population mean under PPS sampling. Calculating the bias and MSE numerically is possible up to the first approximation. A simulation study and four real data are used to evaluate the efficiency of estimators. The numerical results based on a simulation study and real-life data shown that the suggested estimators perform well in terms of least MSE and advanced PRE. Out of all the suggested estimators we examined that the second and fourth suggested estimators outperform the others estimators. The recommended estimators are better in terms of least MSE, as shown by the significant boost in efficiency.
Mathematical Subject Classification: 62D05