经验不确定分布一致性检验方法研究

Consistency Test for the Empirical Uncertainty Distribution

经验不确定分布一致性检验是在不确定分布未知的情况下,利用专家经验数据对不确定分布进行推断的一种非参数检验方法,是不确定统计领域参数估计和回归分析的基础和前提。本文主要研究了几种专家经验不确定分布的一致性检验方法。首先,简述了不确定统计和专家经验数据的基本理论;其次,利用专家经验数据系统分析了两组专家的经验分布是否存在显著性差异的Mann-Whitney U检验法、Kolmogorov-Smirnov检验法、游程检验法和极端反应检验法;再次,研究了多组专家经验数据是否存在显著性差异的Kruskal-Wallis检验法和Jonckheere-Terpstra检验法。并借助Matlab 7.0和SPSS 20,利用概率统计中抽样分布理论进行实证分析。

The research on consistency test for empirical uncertainty distribution is nonparametric statistical inference for an unknown uncertainty distribution by the expert＇s experimental data, that is the basis and premise of parameter estimation and regression analysis in uncertain statistics. The emphasis in this paper is mainly on the research of consistency test for empirical uncertainty distribution. Firstly, the basic theory of uncertain statistics and expert＇s experimental data are described. Secondly, by collecting and interpreting two expert＇s experimental data, we establish some method whether there is a significant difference in two empirical distribution, such that Mann-Whitney U test method, Kolmogorov-Smirnov test method, run test method and moses extreme reactions. Thirdly, Kruskal-Wallis test method and Jonckheere-Terpstra test method about multiple expert＇s empirical distribution consistency test are studied. Finally, by Matlab7.0 and SPSS 20, we empirical analysis of various methods based on the theory of sampling distribution in probability and statistics.