Some properties of stop-loss moments under biased sampling.

The stop-loss moments have generally been used as useful summary measures for analyzing the data which exceeds specific threshold levels. In many scientific studies, the investigator cannot record the sampling units with equal probability, and in such a scenario, the selected sample units appear with unequal probability, in other words with different weights, which leads to a biased or weighted sampling. In the present study, we examine the usefulness of stop-loss moments in biased sampling. The application of the weighted stop-loss moments in analyzing biased data has been investigated and compared using different empirical estimators through simulated and real data sets.