Estimation of Finite Population Mean under Probability-Proportional-to-Size Sampling in the Presence of Extreme Values

This article developed an estimator for finite population mean under probability-proportional-to-size sampling in the presence of extreme values. Theoretical properties such as bias, variance, and consistency are derived. Monte Carlo simulations were performed to assess the consistency and efficiency of the proposed estimator. It is found that the proposed estimator is more efficient than the competing estimators for all values of c between 0 and 1. The gain in precision of the proposed estimator is much higher than that of its competitors for small values of c. Empirical applications of the proposed estimator are illustrated using three real data sets, and the results revealed that the proposed estimator performed better than the conventional and Sarndal (1972) estimators.