GM(1,1)和马氏链模型预测图书馆借阅量.doc

基于马尔科夫链与灰色GM(1,1) 的图书借阅量的预测模型的研究 摘 要 通过分析图书借阅量的特点，建立了基于马尔科夫链的图书借阅量的预测模型和灰色GM(1,1)模型预测，并对两种模型预测结果相对比分析，得出马尔柯夫链理论适用于预测随机波动大的动态过程，在这一点上恰恰可以弥补灰色预测的局限.马氏链预测对象要求具有马氏链和平稳过程等均值的特点，而客观世界中的预测问题大量是随时间变化或呈某种变化趋势的非平稳过程. 如果采用灰色GM（l，l）模型对预测问题的时序数据进行拟合，找出其变化趋势，则可以弥补马氏链预测的局限，而在灰色预测的基础上进行马尔柯夫预测，又可以弥补灰色预测对随机波动大的数据序列预测准确度低的缺陷。从而两种模型相互结合可以较准确地图书馆借阅量情况进行预测。 关键词：图书借阅量 马尔科夫链 预测 灰色系统模型GM(1,1) Abstract Through the analysis of the characteristics of library, based on markov chain of books borrowing amount of prediction model and gray GM (1, 1) model, and predicted the two kinds of model to predict the results relatively ratio analysis, have to turn KeFu chains theory applies to predict the dynamic process of random fluctuation big, at this point just can make up for the limitations of grey prediction. Markov chain prediction object requires a markov chain and a smooth process, the characteristics of the mean value, and the objective world of the prediction problem is change over time or show a change trend of non-stationary process. If using gray GM (l, l) model to predict the timing problem fitting to the data to find its change trend, it can make up for the limitations of markov chain prediction, and in the grey forecasting is conducted on the basis of markov forecast, and can make up for grey forecasting of random fluctuation large data sequence the defects of low prediction accuracy. Thus two combined with model can accurately the library borrowing amount situation forecast. Key words: book loan quantity Marco chain prediction gray system model GM (1,1) 1模型假设 5 2模型的建立与求解 6 2.1 马尔可夫预测法基本原理及方法 6 2.1.1 马尔可夫预测法概述 6 2.1.2 马尔科夫链的特点[2] 6 2.1.3 马尔科夫预测法基本概念[3-5] 6 2.1.3．1状态 6 2.1.3.2状态转移过程 7 2.1.3.3马尔科夫过程 7 2.1.3.4马尔科夫链 7 2.1.3.5状态转移概率 7 2.1.3.6概率矩阵 7 2.1.3.7状态转移概率矩阵 8 2.1.4马尔科夫链预测算法步骤 8 2．1.5 利用马尔科夫预测法分析实际案例 9 2.2灰色系统GM（1,1）模型预测借阅量 12 2.2.1 灰色系统GM ( 1, 1) 模型 12 2.2.2后验差检验 14 2.2.3 实例分析 15 3马氏链模型与灰色系统GM（1,1）模型的比较与评价及改进 18 4结论 19 参考文献 21 附录 22 引言： 一般来说，管理的关键是决策，而预测是决策的前提。借阅量是图书馆业务统计中的重要指