This manuscript investigates the stochastic comparisons of the second-order statistics from dependent and heterogeneous general semi-parametric family of distributions observations. Some sufficient conditions on the usual stochastic order of the second-order statistics from dependent and heterogeneous observations are established under the p-larger order and the reciprocally majorization order. Some numerical examples are given to illustrate the theoretical findings. In addition, the results of the Theorem are applied to two important models. Finally, we use a group of real data for empirical analysis to carry out reliability analysis.

翻译：本文研究了来自相依异质广义半参数分布族观测值的二阶统计量的随机比较。在p-较大序和互反优超序下，建立了关于相依异质观测值二阶统计量常见随机序的一些充分条件。文中给出了若干数值算例以阐明理论结果。此外，将定理的结论应用于两个重要模型。最后，我们使用一组真实数据进行实证分析以开展可靠性分析。