We provide in this paper sufficient conditions for comparing, in terms of the increasing concave order, some income random variables based on linear combinations of order statistics that are relevant in the framework of social welfare. The random variables under study are weighted average incomes of the poorest and, for some particular weights, their expectations are welfare measures whose integral representations are weighted areas underneath Bonferroni curves.

中文翻译：

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增加订单统计线性组合的凹序并应用于社会福利

我们在本文中提供了充分条件来比较一些在递增凹阶方面的收入随机变量，这些随机变量基于社会福利框架中相关的阶数统计的线性组合。研究中的随机变量是最贫困人口的加权平均收入，对于某些特定权重，他们的预期是福利措施，其积分表示是 Bonferroni 曲线下方的加权区域。