问题如下:
Which of the following statements is the most accurate about the relationship between a normal distribution and a Student’s t distribution that have the same mean and standard deviation?
选项:
A.They have the same skewness and the same kurtosis.
B.The Student’ t distribution has larger skewness and larger kurtosis.
C.The kurtosis of a Students t distribution converges to that of the normal distribution as the number of degrees of freedom increases.
D.The normal distribution is a good approximation for the Student’s t distribution when the number of degrees of freedom is small.
解释:
The two distributions have the same skewness of zero but the Student’ t has lower kurtosis. As the number of degrees of freedom increases, the Student’s t distribution converges to the normal distribution, so C is the correct answer.
正态分布与t分布,在两者的均值与标准差相同的时候,相对于正态分布,t分布峰度低,并且尾部肥,对吗?那么,在讲Kurtosis的时候,假设方差相同,得出的结论是:低峰→薄尾。不矛盾吗?请问老师,我是哪里理解错了?