通过α变换预测生命表死亡人数的年龄分布

Han Lin Shang, Steven Haberman
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摘要

我们引入了一种被称为{\alpha}变换的组成幂变换,来模拟和预测生命-死亡计数的时间序列,其中可能在较大年龄段观测到零计数。作为等距对数比率变换(即{\alpha} = 0)的一般化,{\alpha}变换依赖于{\alpha}调谐参数,该参数可以通过数据驱动的方式确定。利用澳大利亚从 1921 年到 2020 年特定年龄段的生命表死亡人数,{\alpha}变换可以产生比对数变换更准确的短期点预测和区间预测。生命表死亡人数预测准确性的提高,对于人口学家和政府规划人员估计生存概率和预期寿命,以及精算师确定不同初始年龄和成熟期的年金价格和储备金,都具有重要意义。
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Forecasting age distribution of life-table death counts via α-transformation
We introduce a compositional power transformation, known as an {\alpha}-transformation, to model and forecast a time series of life-table death counts, possibly with zero counts observed at older ages. As a generalisation of the isometric log-ratio transformation (i.e., {\alpha} = 0), the {\alpha} transformation relies on the tuning parameter {\alpha}, which can be determined in a data-driven manner. Using the Australian age-specific period life-table death counts from 1921 to 2020, the {\alpha} transformation can produce more accurate short-term point and interval forecasts than the log-ratio transformation. The improved forecast accuracy of life-table death counts is of great importance to demographers and government planners for estimating survival probabilities and life expectancy and actuaries for determining annuity prices and reserves for various initial ages and maturity terms.
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