A modified extreme value perspective on best-performance life expectancy
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A modified extreme value perspective on best‑performance life expectancy Jackie Li1 · Jia Liu2
© Springer Nature B.V. 2020
Abstract 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. Keywords Best-performance life expectancy · Generalised extreme value theory · Archimedean copulas · Maxima
* Jackie Li [email protected] Jia Liu [email protected] 1
Department of Actuarial Studies and Business Analytics, Macquarie University, Sydney, Australia
2
School of Business, Western Sydney University, Sydney, Australia
13
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J. Li, J. Liu
Introduction As population ageing is increasingly becoming one of the top global economic challenges in the twenty-first century to be resolved by governments, insurers, and pension plan sponsors, the study on life expectancy has never been more compelling and crucial. A salient discovery was made by Oeppen and Vaupel (2002) that the highest female period life expectancy at birth among countries in the world each year has been persistently growing by about 0.24 years annually for 160 years since 1840. They also described the life expectancy of the leading country in a given year as being ‘best-performance’ or ‘best-practice’. Vallin and Meslé (2009) expanded the study with data from more countries and for a longer period covering 1750–2005. They showed that instead of using a single linear trend, a closer fit may be achieved by breaking the trend down into four linear segments. Shkolnikov et al. (2011) studied the concept of best-performance life expectancy (BPLE) through a cohort perspective whereas Wilson (2011) compared the BPLE trend with the life expectancy trends of five groups of countries differentiated by g
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