Estimating moments of a selected Pareto population under asymmetric scale invariant loss function

摘要

AbstractConsider independent random samples from$$(kge 2)$$(k≥2)Pareto populations with the same known shape parameter but different scale parameters. Let$$X_i$$Xibe the smallest observation of theith sample. The natural selection rule which selects the population associated with the largest$$X_i$$Xiis considered. In this paper, we estimate the moments of the selected population under asymmetric scale invariant loss function. We investigate risk-unbiased, consistency and admissibility of the natural estimators for the moments of the selected population. Finally, the risk-bias’s and risks of the natural estimators are numerically computed and compa