中国人口预测

信息计算科学论文编号:XXLW096 论文字数:13004,页数:37

 目  录
摘  要 I
Abstract II
目  录 III
第一章  绪论 1
1.1  研究动机与目的 1
1.2  研究背景 1
第二章  模型假设 2
第三章  模型建立与求解 3
3.1  人口增长的短期的预测 3
3.1.1 指数增长模型(Malthus模型) 3
3.1.2 Logistic模型(Malthus模型改进) 4
3.1.3 一元线性回归模型 6
3.2  人口增长的中期的预测 10
3.2.1 灰色系统模型 10
3.3  人口增长的长期预测 14
3.3.1 多元变量的线性回归模型(采用逐步回归法) 14
3.3.2 多变量自适应回归样条 16
第四章  模型评价 25
参考文献 26
致  谢 27
附  录 28

摘  要
 本文讨论中国未来人口数量的预测及评价问题。基于一定的假设，建立数学模型，对全国人口作出预测，有利于构建和谐社会。
 本文分别从短、中和长期进行预测，采用了三种不同的算法。短期预测中，利用Malthus和Logistic微分方程人口模型。一元线性回归模型，能比较精确地进行短期预测。最后分别对这三种模型预测出来的数据与官方数据进行比较。在中期的预测我们采用了灰色预测模型中的GM(1,1)模型,该模型以“部分信息已知，部分信息未知”的“小样本”、“贫信息”不确定性系统为研究对象，尽管信息量比较少，但对中短期预测也有较好的效果.而长期的预测则采用多元线性回归模型中的逐步回归方法进行预测，并考虑了出生率和死亡率对人口数量的影响。最后我们还用多变量自适应回归样条，其算法为模型构造策略类似于前向逐步线性回归，该模型过度拟合数据，为此使用一个后向删除过程。多变量自适应回归样条通过选取跨不同的年段来实现短中期的预测，效果很好，跟中国的人口增长趋势相吻合，因为数据较少，算法不能实现长期预测。
 模型改进：微分方程模型要得到更加好的预测精度，应该划分人群，比如分年龄组、城镇乡组、性别组等，区别对待，考虑各自的共性。多元线性回归模型中的逐步回归方法可以考虑更多的变量。
 
关键词：Malthus模型 灰色预测模型 多变量自适应回归样条 MATLAB软件 多元逐步线性回归

Abstract
 This article will discuss China in the future the population quantity forecast and the appraisal question. Based on certain supposition, establishes the mathematical model, makes the forecast to the population, is advantageous in the construction harmonious society.
 This article from short, neutral carries on the forecast for a long time separately, has used three different algorithms. In the short-term predict that uses Malthus and the Logistic differential equation population model. A Yuan linear regression model, can carry on the short-term forecast quite precisely. Finally forecast separately to these three kind of models the data and the official data carry on the comparison. In the intermediate stage forecast that we have used in the gray forecast model GM(1,1) model, this model by “partial informations known, partial informations unknown” “the small sample”, “the poor information” the uncertainty system is the object of study, although the information content are quite few, but to the short and medium term forecast that also has the good effect. But the long-term forecast uses in the multi-dimensional linear regression model the stepwise regression method to carry on the predict that and has considered the birth rate and the mortality rate to the population quantity influence. Finally we also use the multivariable auto-adapted return transect, its algorithm is similar for the model construction strategy to the forward gradually linear regression, this model fits the data excessively, for this reason uses a backward delete procedure. The multivariable auto-adapted return transect through selects the cross different year section to realize the short intermediate stage predict that the effect is very good, tallies with China's population growth tendency, because the data are few, the algorithm cannot realize the long-term forecast.
 model improvement: The differential equation model must obtain the better forecast precision, should divide the crowd, for instance a minute age group, the city towns and villages group, the sex group and so on, the differential treatment, considers the respective general character. In the multi-dimensional linear regression model's stepwise regression method may consider more variables.
 
Keywords: Malthus model grey prediction model multivariate adaptive regression splines MATLAB software Multiple linear regression