ABSTRACT

The Lee–Carter model is a well-known model in modeling mortality. We aim to compare three probability models (Poisson, negative binomial and binomial) based on the Generalized Linear Model (GLM) framework of the Lee–Carter model. These models are applied to mortality data for 10 selected countries (Japan, United States, United Kingdom, Australia, Sweden, Spain, Belgium, Canada, Netherlands and Bulgaria) and the fit of these models is assessed using the deviance statistics and standardized residuals against fitted value plot. Among these three models, the negative binomial Lee–Carter model gave the best fit based on the deviance statistics and estimates of the log of deaths.

摘要

Lee-Carter 模型是死亡率建模的著名模型。我们旨在基于 Lee-Carter 模型的广义线性模型 (GLM) 框架比较三种概率模型（泊松、负二项式和二项式）。这些模型应用于 10 个选定国家（日本、美国、英国、澳大利亚、瑞典、西班牙、比利时、加拿大、荷兰和保加利亚）的死亡率数据，并使用偏差统计和标准化残差评估这些模型的拟合度拟合值图。在这三个模型中，负二项式 Lee-Carter 模型基于偏差统计和死亡对数估计给出了最佳拟合。