中國人口預測

信息計算科學論文編號:XXLW096 論文字數:13004,頁數:37

 目  錄
摘  要 I
Abstract II
目  錄 III
第一章  緒論 1
1.1  研究動機與目的 1
1.2  研究背景 1
第二章  模型假設 2
第三章  模型建立與求解 3
3.1  人口增長的短期的預測 3
3.1.1 指數增長模型(Malthus模型) 3
3.1.2 Logistic模型(Malthus模型改進) 4
3.1.3 一元線性回歸模型 6
3.2  人口增長的中期的預測 10
3.2.1 灰色系統模型 10
3.3  人口增長的長期預測 14
3.3.1 多元變量的線性回歸模型(采用逐步回歸法) 14
3.3.2 多變量自適應回歸樣條 16
第四章  模型評價 25
參考文獻 26
致  謝 27
附  錄 28

摘  要
 本文討論中國未來人口數量的預測及評價問題。基于一定的假設，建立數學模型，對全國人口作出預測，有利于構建和諧社會。
 本文分別從短、中和長期進行預測，采用了三種不同的算法。短期預測中，利用Malthus和Logistic微分方程人口模型。一元線性回歸模型，能比較精確地進行短期預測。最后分別對這三種模型預測出來的數據與官方數據進行比較。在中期的預測我們采用了灰色預測模型中的GM(1,1)模型,該模型以“部分信息已知，部分信息未知”的“小樣本”、“貧信息”不確定性系統為研究對象，盡管信息量比較少，但對中短期預測也有較好的效果.而長期的預測則采用多元線性回歸模型中的逐步回歸方法進行預測，并考慮了出生率和死亡率對人口數量的影響。最后我們還用多變量自適應回歸樣條，其算法為模型構造策略類似于前向逐步線性回歸，該模型過度擬合數據，為此使用一個后向刪除過程。多變量自適應回歸樣條通過選取跨不同的年段來實現短中期的預測，效果很好，跟中國的人口增長趨勢相吻合，因為數據較少，算法不能實現長期預測。
 模型改進：微分方程模型要得到更加好的預測精度，應該劃分人群，比如分年齡組、城鎮鄉組、性別組等，區別對待，考慮各自的共性。多元線性回歸模型中的逐步回歸方法可以考慮更多的變量。
 
關鍵詞：Malthus模型 灰色預測模型 多變量自適應回歸樣條 MATLAB軟件 多元逐步線性回歸

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