中国老年人口死亡模型

Mortality Model of Elderly Population in China

中国老年人口的规模与比例急剧上升,预期寿命不断延长,老年人口死亡率变动趋势引起社会的广泛关注。本文采用1982年、1990年、2000年和2010年四次人口普查数据,选用10种参数模型分析比较65岁及以上老年人口累计死亡概率。研究发现逻辑斯蒂模型、冈泊茨-麦克汉姆模型、威布尔模型和广义极值模型能较好地拟合老年人口累计死亡概率。通过比较模型拟合结果与观测值之间的差异发现逻辑斯蒂模型整体上能较好地体现中国老年人口死亡模式;冈泊茨-麦克汉姆、广义极值、逆高斯、对数-逻辑斯蒂、对数-正态和威布尔六种模型的拟合结果在低龄老年阶段和高龄老年阶段低于观测值,在中龄老年阶段高于观测值;冈泊茨模型的拟合结果在低龄老年阶段和高龄老年阶段高于观测值;指数模型和伽玛模型的拟合结果在整个老年阶段均低于观测值。将最高年龄组由100岁拓展到130岁,发现逻辑斯蒂模型和威布尔模型预测结果较好。本文的研究结果为拟合不同老年阶段死亡模式选择合适的模型提供了方法借鉴。

The size and proportion of China’s elderly population have risen sharply,and life expectancy continues to increase.The trend of mortality among the elderly population has attracted social attention.This research analyzes and compares the cumulative probability of death of the elderly population aged 65 and above using four census data and ten models.The Logistic,Generalized Extreme Value,Gompertz Makeham,and Weibull models are shown to better fit the elderly population’s cumulative probability of death.By comparing the difference between the model fitting results and the observed values,the Logistic model can better describe the mortality pattern of the elderly population in China.The fitting results of Gom⁃pertz-Makeham,Generalized Extreme Value,Inverse Gaussian,Log-logistic,Log-normal and Weibull models are lower than the observed values in the youngest-old age and oldest-old age,but higher than the observed values in the middle-old age.The Gompertz model’s fitting results are higher than the observed values in the youngest-old age and oldest-old age.The Exponential and Gamma models’fitting results are lower than the observed values.By extrapolating the maximum age group from 100 to 130 years,the Logistic and Weibull models perform well.The findings of this paper provide a reference for the selection of appro⁃priate models in different old age groups.