Modeling and forecasting subnational age distribution of death counts

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 nonnegative 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 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 for determining annuity prices for various ages and maturities.