that they have a similar performance when using x and x2. However,Fr(t),Fd(t) andFdm(t) are less efficient whenx2is used at the estimation stage. Similar conclusions can be derived from the exponential populations, i.e., proposedestimators have a similar performance under different scenarios and they generally are the most efficient estimators.Model (3) does not hold for the exponential populations and alternative estimators are less efficient in this situation.From Table 2 we also observe that the gain in efficiency of the proposed estimators over alternative estimatorsdepends on α. For this reason, we also considered a global measure of performance of the estimators across variousquantiles. Following [18], we calculated the average root mean square error (AVRMSE), where