论文总字数：18904字

摘 要

中国正在处于社会主义初级阶段快速发展、实现全面小康的重要时期，但是，人口数量庞大、自然资源相对不充足、环境承受能力相对较弱是我国现阶段的基本国情，短时间是难以改变。因此，准确的预测未来的人口走向与数量尤为重要，有助于国家出台制定相应的政策来应对未来的国情。考虑到其重要性及影响因素的复杂性，准确的研究人口趋势的变化具有十分重要的理论和指导意义。

本文首先以阻滞增长模型、灰色模型、马尔萨斯人口模型为研究工具，对这三种模型进行简单的理论介绍。再是利用三种模型对1980-2007年的人口数进行拟合，结果显示，并不是只有一种模型就可以很好地拟合数据，三种模型分段拟合可以使误差达到最低的标准。然后利用1980-2007拟合时得出的参数进行未来十五年的预测，选取2008-2017年的预测结果与实际情况进行对比分析，计算出每年的相对误差，通过相对误差的大小比对，可以得出最优的预测结果。最后通过三种模型对2018-2022年的预测来分析未来的人口变化情况。

通过模型分析与多因素考虑，本文利用马尔萨斯人口模型进行预测时，选定的增长率过高，忽略了我国人口政策的影响，使得预测的误差比较大，适当调整增长率后进行预测，可以得到更相近的结果；灰色模型短期预测性较高，从2006年之后，我国人口增长率才趋于稳定，在2006年之前，我国人口一直处于高速增长的状态，增长率较大，因此，灰色模型使用累加的方法，无法准确的体现人口的变动，而且其是在没有自然灾害等情况下建立的，不适合长期预测；而阻滞增长模型是将增长率看成每年人口总数的一个减函数，其只有在年末总人口数离人口环境最大容纳量很远的情况的条件适用。因此，无法说明哪种模型更有优越性。

本文最后针对人口问题的研究进行了一些总结和意见。

关键词：人口模型预测模型 阻滞增长模型 灰色模型 马尔萨斯模型 相对误差

The population model of China and its improvement

Abstract

China is now in an important rapid of development and all-round prosperity in the primary stage of socialism. China's basic national conditions at this stage are large population, relatively insufficient resources and weak environmental capacity, which will be difficult to change in a short time. Therefore, it is particularly important to accurately predict the future population trend and quantity, which is helpful to formulate corresponding policies to cope with the future national conditions. Allowing for its importance and complexity of influencing factors, it is of huge impact to study the change of population trend accurately. In this paper, as the research tools, Logistic growth model, Grey models, Malthusian model are briefly introduced. Then, three models are used to fit the function of the population from 1980 to 2007. The result shows that not one model can fit the function well, on the contrary, the piecewise fitting function of the three models can make the error reach the lowest standard. After that, the parameters obtained by the fitting function of 1980-2007 are used to predict the future decades, and the predicted results are compared with the actual situation to calculate the relative errors. By comparing the relative errors, the optimal fitting results can be obtained.

Through model analysis and multi-factor consideration, when we used the Malthusian model to make the prediction, the selected growth rate is too high because the influence of China's population policy is ignored. As a result, the prediction error is relatively large. While the growth rate is adjusted appropriately, a more similar result can be chalked up. The accuracy of Grey short-term forecasting model is higher. After 2006, the growth rate of population tends to be at the same state. In the years before 2006, the population has been in the condition of vigorous growth and the growth rate is bigger. Therefore, the Grey model using the cumulative method can not reflect the changes of population accurately, and it is established in the absence of natural disasters, which is not suitable for long-term forecast. Logistic growth model regards the growth rate as a minus function of the total population of each year, which simplifies the calculation. Therefore, it is impossible to indicate which model is more advantageous.

Finally, some proposals are submitted for the study of population problem.

Keywords: Population prediction; Logistic growth model; Grey models; Malthusian model; The relative error

目录

摘要 I

Abstract II

第一章 引言 1

1.1 研究目的及意义 1

1.2 研究相关背景 1

1.2.1 国外相关研究回顾 1

1.2.2 国内相关研究回顾 2

1.3 本文的研究方法及创新点 3

第二章 模型的理论概述，样本选取 5

2.1模型的理论概述 5

2.1.1 logistic阻滞增长模型 5

2.1.2灰色模型GM(1,1) 5

2.1.3马尔萨斯人口模型Malthusian model 7

2.1.4模型的检验方法及精度标准 7

2.2 样本选取 8

第三章 三种模型拟合结果和检验 10

3.1 样本数据分析 10

3.2 阻滞增长模型的拟合和检验 10

3.3 灰色模型的拟合和检验 12

3.4马尔萨斯模型的拟合和检验 13

第四章 模型分段拟合预测分析 15

4.1 模型拟合 15

4.2人口预测结果分析 15

第五章 结论与建议 18

参考文献 19

致谢 20

第一章 引言

1.1 研究目的及意义

自建国以来70年的时间内，中国人口经历了快速增长、计划生育、双独二孩、单独二孩、全面二胎等人口政策的调整，中国人口规模一直在增长，但是自从计划生育政策的严格执行调整到双独二孩政策以来，关于中国人口的规模即将进入负增长、劳动力已经供给不足、进入老龄化社会等议论纷纭。

请支付后下载全文，论文总字数：18904字