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

摘要: 本文通过基于非参数核密度的半参数估计法以及与经验Copula函数之间的平方欧式距离对学生成绩的极值与均值建立了Gumbel Copula模型。利用基于Gumbel Copula函数的相关性度量研究了学生成绩最高分、最低分与平均分的相关性，得到最低分与平均分的Kendall秩相关系数与上尾相关系数均稍高于最高分的结论。

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.