﻿ 基于Copula函数的学生成绩极值与均值的相关性研究 The Study of the Correlation between Extreme Value and Mean Value of the Student Achievement Based on Copula Function

Vol.06 No.04(2017), Article ID:21399,7 pages
10.12677/AAM.2017.64061

The Study of the Correlation between Extreme Value and Mean Value of the Student Achievement Based on Copula Function

Hong Chang, Fuxia Xu*

School of Science, Tianjin Polytechnic University, Tianjin

*通讯作者。

Received: Jun. 25th, 2017; accepted: Jul. 15th, 2017; published: Jul. 18th, 2017

ABSTRACT

Based on the semiparametric estimation method of nonparametric kernel density and the square and Euclidean distance with empirical Copula functions, the Gumbel Copula model is established for the extreme and mean value of the student achievement. We rely on the Gumbel Copula function to investigate the correlation between the highest score, the lowest score and the average score. It turns out that the Kendall rank correlation coefficient and the upper tail correlation coefficient are slightly higher than the highest points.

Keywords:Copula Function, Kerneldensity Estimation, Semiparametric Estimation, Rank Correlation, Tail Correlation

1. 引言

2. 问题的分析

Table 1. The highest score, the lowest score and the average score of points in some classes

Table 2. Skewness, kurtosis and normality test results

Figure 1. Frequency distribution histogram

3. Copula函数模型的建立

3.1. 参数估计

Figure 2. Kernel density estimation

Figure 3. Estimation of nuclear distribution

3.2. 模型的选取

(1)

Table 3. Parameter estimation results of Copula functions with the highest score and the average score

Table 4. Parameter estimation results of Copula functions with the lowest score and the average score

Table 5. Square Euclidean distance of Copula functions with the highest score and the average score

Table 6. Square Euclidean distance of Copula functions with the lowest score and the average score

Figure 4. The distribution function of Empirical Copula

(2)

(3)

4. 相关性分析

Figure 5. The density function graph and distribution function graph of Gumbel-Copula between the highest score and average score

Figure 6. The density function graph and distribution function graph of Gumbel-Copula between the lowest score and average score

Table 7. Correlation coefficient based on Gumbel Copula

5. 结论

The Study of the Correlation between Extreme Value and Mean Value of the Student Achievement Based on Copula Function[J]. 应用数学进展, 2017, 06(04): 508-514. http://dx.doi.org/10.12677/AAM.2017.64061

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