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Modeling old-age mortality risk for the populations of Australia and New Zealand: An extreme value approach. (English) Zbl 1217.62177

Summary: Old-age mortality for populations of developed countries has been improving rapidly since the 1950s. This phenomenon, which is often referred to as ‘rectangularization’ of mortality, implies an increased survival at advanced ages. With this increase come different challenges to actuaries, economists and policy planners. A reliable estimate of old-age mortality would definitely help them develop various demographic and financial projections. Unfortunately, data quality issues have made the modeling of old-age mortality difficult and we need a method that can extrapolate a survival distribution to extreme ages without requiring accurate mortality data for the centenarian population.
We focus on a method called the threshold life table which systematically integrates extreme value theory to the parametric modeling of mortality. We apply the threshold life table to model the most recent period (static) mortality rates for the populations of Australia and New Zealand. We observe a good fit to the raw data for both populations. We then extend the model to predict the highest attained age, which is commonly referred to as ‘omega’ or \(\omega \) in the actuarial literature, for the populations of Australia and New Zealand. On the basis of the threshold life table, the central estimates of \(\omega \) for Australia and New Zealand are 112.20 and 109.43, respectively. Our estimates of \(\omega \) are reasonably consistent with the validated supercentenarian in these countries.

MSC:

62P10 Applications of statistics to biology and medical sciences; meta analysis
91D20 Mathematical geography and demography
62G32 Statistics of extreme values; tail inference

Software:

Human Mortality
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