problems and provide scientific evidence for government to control the population.
KEY WORDS: Discrete Population Development Equations, Fertility, Mortality, Immigration, Population Forecast, Age Structure Population Tree
上海交通大学 硕士学位论文 人口年龄结构模型建模和预测 姓名：虞丽萍 申请学位级别：硕士 专业：控制理论与控制工程 指导教师：袁景淇 20070101
人口年龄结构模型建模和预测
摘
要
人口是一个动态系统。人口变化对未来经济、社会的发展有着直接 的影响。人口年龄结构是人口研究的重要指标之一，人口年龄结构发展 趋势的预报对人口政策的制定有着非常重要的作用。本文以离散形式的 人口发展方程为主模型。在此基础上，分别建立了生育率、死亡率和迁 移模型，以预测人口生育率、死亡率、流动人口和人口年龄结构的变化 趋势。与传统模型相比，本文所提出的基于随机分布函数的生育率组合 模型和死亡率分段模型使模型精度得到了进一步的提高。 本文以中国历年统计数据为原始数据，验证了主模型和各子模型的 有效性，并预测了 2015 年上海市人口年龄结构，绘制了人口年龄树。 人口年龄树树形反映了人口结构的健康状态。通过分析人口年龄树的变 化趋势，可以了解人口结构所存在的问题，为政府调控人口提供科学依 据。 关键词：离散人口发展方程，生育率，死亡率，流动人口，人口预测， 人口年龄树
表格目录
表 1 Lognormal 和 Poisson 分布模型描述分孩次的年龄别生育率 ······················· 22 表 2 组合模型参数的估计值（最小二乘法） ······················································ 25 表 3 总和生育率 GM（1,1）模型预测结果 ·························································· 31 表 4 2003 年中国分年龄组死亡率统计数据 ·························································· 34 表 5 1989 年中国人口死亡率各模型拟合均方根误差比较 ··································· 39 表 6 1994 年中国人口死亡率各模型拟合均方根误差比较 ··································· 39 表 7 1998 年中国人口死亡率各模型拟合均方根误差比较 ··································· 39 表 8 2001 年中国人口死亡率各模型拟合均方根误差比较 ··································· 40 表 9 中国历年人均国民生产总值 GNP ································································· 43 表 10 上海市第五次人口普查外来人口年龄分布 ················································ 53 表 11 上海市主要年份人口迁移数据 ···································································· 55 表 12 上海市人口迁移数据预测 ············································································ 56 表 13 2004 年中国人口年龄结构 ············································································ 59 表 14 人口年龄结构类型（国际通用标准） ······················································ 59 表 15 上海市总和生育率预测 ················································································ 64 表 16 上海市 2015 年人口年龄树相关数据 ·························································· 65
片目录
图 1 人口金字塔 ······································································································· 5 图 2 人口年龄树 ······································································································· 6 图3 图4 人口结构的三种类型 ······················································································ 8 人口状态方程控制框图 ················································································ 11
图 5 人口发展方程的数据流图 ·············································································· 12 图 6 三层 BP 神经网络的拓扑结构 ······································································· 16 图7 世代生育率(CFR)与总和生育率(TFR)的比较 ············································ 18 图 8 2000 年分孩次的年龄别生育率模型拟合结果与统计数据比较 ··················· 24 图 9 组合模型、对数正态分布模型及泊松分布模型精度比较 ··························· 27 图 10 不同模型分年龄别生育率误差比较 ···························································· 28 图 11 不同模型对 2004 年分年龄别生育率的预测估计 ········································ 32 图 12 组合模型对 2015 年全国分年龄别生育率的预测······································· 32 图 13 2003 年中国人口死亡率三次样条插值结果与实际数据比较（男） ········· 35 图 14 2003 年中国人口死亡率三次样条插值结果与实际数据比较（女） ········· 36 图 15 2001 年中国人口死亡率分段模型拟合结果与实际数据比较 ·················· 41 图 16 影响人口死亡率的因素 ················································································ 42 图 17 参数 a 估计值································································································ 44 图 18 参数 b 估计值 ······························································································· 44 图 19 参数 c 估计值································································································ 45 图 20 图 21 图 22 图 23 图 24 图 25 图 26 2004 年中国男性分年龄别死亡率预测值与实际值比较 ·························· 46 2004 年中国男性分年龄别死亡率预测值与实际值比较 ·························· 47 2000 年上海市外来人口按年龄别分布图 ················································· 55 2004 年中国人口年龄树 ············································································· 58 2004 年中国人口年龄结构预测值与实际值相对误差 ······························ 58 上海市历年总和生育率 ·············································································· 64 2015 年上海市人口年龄树 ········································································· 65
MODELING AND FORECASTING THE AGE STRUCTURE OF POPULATION
ABSTRACT
The population system is a dynamical system. The trend of a population will affect the development of the society and its economy. The age structure is one of the most important indexes in population research. The forecast of age structure plays an important role in making population policies. A discrete model of population development was applied in this paper. Fertility model, mortality model and immigration model were also established to forecast the fertility, mortality, immigration population and the age structure. Compared with traditional functions, both the composite fertility model which is based on random distribution functions and the segmented mortality model improved the models’ accuracy. Historical Chinese population statistics were used to prove the validity of the models referred in this paper. The age structure of Shanghai in 2015 was forecasted and displayed in a tree-like graph. The shape of the population tree reflects the health condition of its age structure. By analyzing the development trend of the age structure, we can find population