NO.PZ2016062402000014
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.
老师,按照T分布的峰度公式,3(n-2)/(n-4),不是应该大于3吗?应该比这正态分布的峰高才是啊,为什么是低峰肥尾呢?