经验不确定分布一致性检验方法研究
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- 英文论文题名：Consistency Test for the Empirical Uncertainty Distribution
- 论文作者：王志刚 ; 张天一 ; 符一平
- 英文论文作者：Zhigang Wang ; Tianyi Zhang ; Yiping Fu ; Department of Mathematics ; Hainan University
- 年：2016
- 作者机构：海南大学数学系;
- 论文关键词：经验不确定分布 ; 专家经验数据 ; 一致性检验 ; 显著性水平 ; 不确定统计
- 英文论文关键词：Empirical Uncertainty Distribution ; Expert's Experimental Data ; Consistency Test ; Significance Level ; Uncertain Statistics
- 会议召开时间：2016-07-26
- 会议录名称：第十四届中国不确定系统年会、第十八届中国青年信息与管理学者大会论文集
- 语种：中文
- 分类号：O212.1
- 学会代码：QHIS
- 会议名称：第十四届中国不确定系统年会第十八届中国青年信息与管理学者大会
- 会议地点：中国陕西渭南
- 主办单位：中国运筹学会不确定系统分会
- 学会名称：清华大学数学科学系
- 页数：7
- 文件大小：461k
- 原文格式：D
- 会议级别：全国
摘要
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 statisticalinference 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.
The research on consistency test for empirical uncertainty distribution is nonparametric statisticalinference 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.
引文
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[9]Ji X.,Zhou J.,Option Pricing for an Uncertain Stock Model with Jumps,Soft Computing,Vol.19,No.11,3323-3329,2015.
[10]Guo H.,Wang X.,Wang L.,Chen D,Delphi Method for Estimating Membership Function of Uncertain Set,Journal of Uncertainty Analysis and Applications,Vol.4,Article 3,2016.
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[13]Wang Z.,Tian F.,Strong Convergence of Independent Fuzzy Variables Sequence,International Journal of Nonlinear Science,Vol.14,No.4,392-397,2012.
[14]Wang Z.,Ou Y.,Cai B.,Option Pricing Formula for Stock Model,International Journal of Applied Mathematics and Statistics,Vol.27,No.3,49-55,2012.
[15]Fu Y.,Wang Z.,Some Convergence Theorems of Uncertain Sequence,International Journal of Applied Mathematics and Statistics,Vol.44,No.14,372-381,2013.
[16]Wang Z.,Tian F.,A Stock Model for Fuzzy Financial Market.International Journal of Nonlinear Science.Vol.15,No.4,334-339,2013.
[17]Wang Z.,Tian F.,Moments and Tails Inequality of Uncertain Variables,International Journal of Applied Mathematics and Statistics.Vol.42,No.12,148-156,2013.
[18]Wang Z.,A Note of the Expected Value and Variance of Fuzzy Variables.International Journal of Nonlinear Science.Vol.9,No.4§486-492.2010.
[19]Wang H.,Kuang Q.,Approximation of the Tail Event for Weighted Sums of Uncertain Variables and Applications.International Journal of Applied Mathematics and Statistics.Vol.45,No.15,465-472,2013.
[2]Liu B.,Uncertainty Distribution and Independence of Uncertain Processes,Fuzzy Optimization and Decision Making,Vol.13,No.3,259-271,2014.
[3]Liu B,and Yao K,Uncertain multilevel programming:Algorithm and applications,Computers and Industrial Engineering,Vol.89,235-240,2015.
[4]Yao K.,Uncertain Contour Process and Its Application in Stock Model with Floating Interest Rate,Fuzzy Optimization and Decision Making,Vol.14,No.4,399-424,2015.
[5]Peng J,Risk Metrics of Loss Function for Uncertain System,Fuzzy Optimization and Decision Making,Vol.12,No.1,53-64,2013.
[6]Chen X.,Uncertain Calculus with Finite Variation Processes,Soft Computing,Vol.19,No.10,2905-2912,2015.
[7]Zhu Y.,Uncertain fractional differential equations and an interest rate model,Mathematical Methods in the Applied Sciences,Vol.38,No.15,3359-3368,2015.
[8]Yang X.,Gao J.,Some Results of Moments of Uncertain Set,Journal of Intelligent and Fuzzy Systems,Vol.28,No.6,2433-2442,2015.
[9]Ji X.,Zhou J.,Option Pricing for an Uncertain Stock Model with Jumps,Soft Computing,Vol.19,No.11,3323-3329,2015.
[10]Guo H.,Wang X.,Wang L.,Chen D,Delphi Method for Estimating Membership Function of Uncertain Set,Journal of Uncertainty Analysis and Applications,Vol.4,Article 3,2016.
[11]Ha M.,Wang X.,Uncertain Linear Regression Model and its Application,http://orsc.edu.cn/online/130331.
[12]Wang X.,Gao Z.,Guo H.,Uncertain hypothesis testing for two experts empirical data,Mathematical and Computer Modeling,Vol.55,1478-1482,2012.
[13]Wang Z.,Tian F.,Strong Convergence of Independent Fuzzy Variables Sequence,International Journal of Nonlinear Science,Vol.14,No.4,392-397,2012.
[14]Wang Z.,Ou Y.,Cai B.,Option Pricing Formula for Stock Model,International Journal of Applied Mathematics and Statistics,Vol.27,No.3,49-55,2012.
[15]Fu Y.,Wang Z.,Some Convergence Theorems of Uncertain Sequence,International Journal of Applied Mathematics and Statistics,Vol.44,No.14,372-381,2013.
[16]Wang Z.,Tian F.,A Stock Model for Fuzzy Financial Market.International Journal of Nonlinear Science.Vol.15,No.4,334-339,2013.
[17]Wang Z.,Tian F.,Moments and Tails Inequality of Uncertain Variables,International Journal of Applied Mathematics and Statistics.Vol.42,No.12,148-156,2013.
[18]Wang Z.,A Note of the Expected Value and Variance of Fuzzy Variables.International Journal of Nonlinear Science.Vol.9,No.4§486-492.2010.
[19]Wang H.,Kuang Q.,Approximation of the Tail Event for Weighted Sums of Uncertain Variables and Applications.International Journal of Applied Mathematics and Statistics.Vol.45,No.15,465-472,2013.