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.
- Archimedean copulas
- Best-performance life expectancy
- Generalised extreme value theory