We study the so-called best-performance life expectancy from a theoretical perspective by using a generalised theorem of the extreme value distribution. Under the generalised extreme value theorem, we experiment with two mathematical models called copulas to model the relationships between countries, and also test alternative parameterisations to co-model the data of both sexes, incorporating both common and sex-specific parameters. In earlier work on using the extreme value distribution for best-performance life expectancy, all countries were assumed to be independent, and the two sexes were treated separately. In this paper, we apply the generalised extreme value theorem with copulas in order to relax the independence assumption between life expectancies of different countries under extreme events. We find that the two resulting limiting distributions model the data reasonably well and allow us to make future projections with probabilistic intervals. Setting certain common parameters between females and males can also improve the information content and parameter parsimony. In particular, we detect significant dependence between countries and notice that the dependence tends to be stronger for males. Based on the aggregate experience of numerous countries, the projected trends may serve as a reference or an upper bound for life expectancy forecasts of individual countries.

我们通过使用极值分布的广义定理从理论角度研究所谓的最佳性能预期寿命。在广义极值定理下，我们使用称为copulas的两个数学模型进行实验，以建模国家之间的关系，并测试替代参数化以共同建模性别数据，并结合了通用参数和针对性别的参数。在使用极值分配获得最佳表现预期寿命的早期工作中，假定所有国家都是独立的，并且将两性分开对待。在本文中，我们将广义极值定理与copulas结合使用，以放宽不同国家在极端事件下的预期寿命之间的独立性假设。我们发现，由此产生的两个极限分布对数据进行了很好的建模，并允许我们以概率间隔进行未来的预测。在男性和女性之间设置某些通用参数也可以提高信息含量和参数简约性。特别是，我们发现国家之间存在严重依赖关系，并注意到男性的依赖关系往往更强。根据许多国家的总经验，预测趋势可作为单个国家预期寿命预测的参考或上限。我们发现国家之间存在严重的依存关系，请注意，男性的依存关系往往更强。根据许多国家的总经验，预测趋势可作为单个国家预期寿命预测的参考或上限。我们发现国家之间存在严重的依存关系，请注意，男性的依存关系往往更强。根据许多国家的总经验，预测趋势可作为单个国家预期寿命预测的参考或上限。