In actuarial science, it is often of interest to compare stochastically smallest claim amounts from heterogeneous portfolios. In this paper, we obtain the usual stochastic order between the smallest claim amounts when the matrix of parameters (α, λ) changes to another matrix in terms of chain majorization order. By using the Archimedean copula and weak majorization conceptions, we also obtain some conditions for comparison of smallest claim amounts in terms of usual stochastic order.
