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

Abstract

Consider independent random samples from \((k\ge 2)\) Pareto populations with the same known shape parameter but different scale parameters. Let \(X_i\) be the smallest observation of the ith sample. The natural selection rule which selects the population associated with the largest \(X_i\) is 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 compared for \(k=2,3.\)