Stochastic Comparisons of Order Statistics from a Sample Following the Power Lomax Distribution

Abstract

For independent random variables following the Power Lomax distribution in the two-dimensional case: If two independent sets of Power Lomax samples share the same scale parameter, and the matrix formed by their shape parametersαandβsatisfies a specific chain majorization order, the lifetimes of series systems can be compared under the hazard rate order. Under the same conditions, the lifetimes of parallel systems can be compared under the reverse hazard rate order. These results imply that, under specific constraints, we can systematically evaluate the lifetime properties of different system architectures.