Mortality forecasting is crucial for demographic planning and actuarial studies, particularly for predicting population ageing rates and future longevity risks. Traditional approaches largely rely on extrapolative methods, such as the Lee-Carter model and its variants which use mortality rates as inputs. In recent years, compositional data analysis (CoDA), which adheres to summability and non-negativity constraints, has gained increasing attention from researchers for its application in mortality forecasting. This study explores the use of the {\alpha}-transformation as an alternative to the commonly applied centered log-ratio (CLR) transformation for converting compositional data from the Aitchison simplex to unconstrained real space. The {\alpha}-transformation offers greater flexibility through the inclusion of the {\alpha} parameter, enabling better adaptation to the underlying data structure and handling of zero values, which are the limitations inherent to the CLR transformation. Using age-specific life table death counts for males and females in 31 selected European countries/regions from 1983 to 2018, the proposed method demonstrates comparable performance to the CLR transformation in most countries with improved forecast accuracy in some cases. These findings highlight the potential of the {\alpha}-transformation as a competitive alternative transformation technique for real-world mortality data within a non-functional CoDA framework.

翻译：死亡率预测对于人口规划和精算研究至关重要，特别是在预测人口老龄化速率和未来长寿风险方面。传统方法主要依赖于外推法，例如以死亡率为输入的Lee-Carter模型及其变体。近年来，遵循可加性和非负性约束的组合数据分析（CoDA）在死亡率预测中的应用日益受到研究者关注。本研究探讨了使用α变换作为常用中心对数比（CLR）变换的替代方法，用于将Aitchison单纯形中的组合数据转换为无约束的实数空间。α变换通过引入α参数提供了更大的灵活性，使其能更好地适应底层数据结构并处理零值，而这正是CLR变换固有的局限性。使用1983年至2018年间31个选定欧洲国家/地区分性别、分年龄的生命表死亡人数数据，所提出的方法在大多数国家表现出与CLR变换相当的性能，并在某些情况下提高了预测精度。这些发现凸显了α变换作为非函数型CoDA框架中处理实际死亡率数据的一种具有竞争力的替代变换技术的潜力。