Existing mortality forecasting methods focus on age-specific mortality rates, which lie in an unconstrained space and overlook the distributional nature of life-table death counts. Few studies have developed and compared forecasting methods that model the shape and dynamics of the age distribution of deaths, especially at the subnational level, where data quality varies greatly. This paper presents several forecasting methods to model and forecast the subnational age distribution of death counts. The age distribution of death counts has many similarities to probability density functions, which are non-negative and have a constrained integral, and thus live in a constrained nonlinear space. To address the nonlinear nature of objects, we implement a cumulative distribution function transformation that is scale-free and has additional monotonicity. Using subnational Japanese life-table death counts from the Japanese Mortality Database (2025), we evaluate the forecast accuracy of the transformation and forecasting methods. The improved forecast accuracy of life-table death counts implemented here will be of great interest to demographers in estimating regional age-specific survival probabilities and life expectancy, and to actuaries as a foundation for exploring potential applications in determining annuity prices for various ages and maturities.

翻译：现有的死亡率预测方法聚焦于年龄别死亡率，这些方法在无约束空间中展开，忽视了生命表死亡人数的分布特性。鲜有研究开发并比较能够刻画死亡年龄分布形状与动态的预测方法，尤其是在数据质量差异显著的亚国家层面。本文提出了若干预测方法，用于对亚国家层面死亡人数的年龄分布进行建模与预测。死亡人数的年龄分布与概率密度函数具有诸多相似之处：其值非负且积分受约束，因而存在于一个受约束的非线性空间中。为应对对象的非线性特征，我们实施了一种无尺度且具有额外单调性的累积分布函数变换。利用日本死亡率数据库（2025年）中的亚国家层面日本生命表死亡人数数据，我们评估了该变换及预测方法的预测准确性。本文所实现的改进的生命表死亡人数预测准确性，将极大地引起人口学家的兴趣，用于估算区域年龄别生存概率与预期寿命；同时，精算师亦可将其作为基础，探索在确定不同年龄与期限的年金价格方面的潜在应用。