Background: In recent years, lifespan inequality has become an important indicator of population health. Uncovering the statistical properties of lifespan inequality measures can provide novel insights on the study of mortality. Methods: We introduce the ‘Average Uneven Mortality’ (AUM) index, a novel mortality indicator for the study of mortality patterns and lifespan inequality. We prove some new properties of interest, as well as relationships with the ‘e-dagger’ and entropy measures of lifespan inequality. Results: The use of the AUM index is illustrated through an application to observed period and cohort death rates from the Human Mortality Database. We explore the behavior of the index across age and over time, and we study its relationship with life expectancy. The AUM index at birth declined over time until the 1950s, when it reverted its trend; also, the index generally increases with age. Contribution: The AUM index is a normalized version of Vaupel and Canudas-Romo’s e-dagger measure that can be meaningfully compared across countries and over time. Additionally, we derive an upper bound for both e-dagger and the life-table entropy measures, which are novel formal results. Finally, we develop novel routines to compute e-dagger and the standard deviation of lifetimes from death rates, which are often more precise than available software, particularly for calculations involving older ages.

中文翻译：

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平均不均匀死亡率指数：基于寿命不平等的“电子匕首”衡量标准（Marco Bonetti、Ugofilippo Basellini、Andrea Nigri）


背景：近年来，寿命不平等已成为人口健康的重要指标。揭示寿命不平等指标的统计特性可以为死亡率研究提供新的见解。方法：我们引入了“平均不均匀死亡率”（AUM）指数，这是一种用于研究死亡率模式和寿命不平等的新型死亡率指标。我们证明了一些令人感兴趣的新属性，以及与“电子匕首”和寿命不平等的熵度量的关系。结果：AUM 指数的使用通过对人类死亡率数据库中观察到的期间和队列死亡率的应用来说明。我们探索该指数随年龄和时间的变化，并研究其与预期寿命的关系。出生时的 AUM 指数随着时间的推移而下降，直到 20 世纪 50 年代才恢复了趋势；此外，该指数通常随着年龄的增长而增加。贡献：AUM 指数是 Vaupel 和 Canudas-Romo 的电子匕首衡量标准的标准化版本，可以在不同国家和不同时间之间进行有意义的比较。此外，我们得出了电子匕首和生命表熵度量的上限，这是新颖的形式结果。最后，我们开发了新颖的例程来计算电子匕首以及寿命与死亡率的标准差，这些例程通常比现有软件更精确，特别是对于涉及老年人的计算。