We present the lower bounds expressed in standard deviation units on the expectations of the generalized order statistics (gOS) which are based on the parent distributions with the decreasing generalized failure rate. The particular cases are families of distributions with the decreasing density and decreasing failure rate. The bounds are obtained with the use of the projection method applied to functions satisfying some particular conditions and appropriately chosen convex cones. We also provide the attainability conditions. The results are illustrated with the numerical results on the progressively type II censored order statistics, which are one of the special cases of gOS.

中文翻译：

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基于 DGFR 分布的 gOS 预期的急剧下限

我们提出了以标准偏差单位表示的广义阶次统计 (gOS) 期望的下限，该期望基于具有降低的广义失效率的父分布。特殊情况是密度降低和故障率降低的分布族。The bounds are obtained with the use of the projection method applied to functions satisfying some particular conditions and appropriately chosen convex cones. 我们还提供可达性条件。结果用渐进式 II 删失顺序统计的数值结果进行说明，这是 gOS 的特殊情况之一。