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124356155 · 2020年02月16日

问一道题: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.

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?

3 个答案

quietvivian · 2020年05月14日

quietvivian · 2020年05月14日

峰度跟分布图形的高度无关,峰度是尾部的面积,随着自由度n的上升,t分布的峰度3(n-2)/(n-4)是下降的,在图形上表现的是尾部与标准正态分布越来越拟合,同时图形的高点上升与正态分布的高点趋近(所以峰度与图形里的高点无关)

orange品职答疑助手 · 2020年02月17日

同学你好。t分布比较特殊,它的特征是“矮峰肥尾”。而其他分布,一般会呈“高峰肥尾、矮峰瘦尾”的特征。

df自由度升高,t分布的峰度会降低,然后它会更高、更接近正态分布,

Roxanne_104 · 2020年03月10日

老师,我没懂,t分布会降低,它会变高?

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NO.PZ2016062402000014 问题如下 Whiof the following statements is the most accurate about the relationship between a normstribution ana Stunt’s t stribution thhave the same meanstanrviation? A.They have the same skewness anthe same kurtosis. B.The Stunt’ t stribution hlarger skewness anlarger kurtosis. C.The kurtosis of a Stunts t stribution converges to thof the normstribution the number of grees of freem increases. The normstribution is a gooapproximation for the Stunt’s t stribution when the number of grees of freem is small. The two stributions have the same skewness of zero but the Stunt’ t hlower kurtosis. the number of grees of freem increases, the Stunt’s t stribution converges to the normstribution, so C is the correanswer. t分布正常是比正态分布离散的,题目里说T和Z方差一致时,我理解就是n已经大到T趋近于Z的情况了,为什么A不对呢

2022-09-05 00:28 2 · 回答

NO.PZ2016062402000014 The Stunt’ t stribution hlarger skewness anlarger kurtosis. The kurtosis of a Stunts t stribution converges to thof the normstribution the number of grees of freem increases. The normstribution is a gooapproximation for the Stunt’s t stribution when the number of grees of freem is small. The two stributions have the same skewness of zero but the Stunt’ t hlower kurtosis. the number of grees of freem increases, the Stunt’s t stribution converges to the normstribution, so C is the correanswer.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?

2022-03-17 01:17 2 · 回答

自由度决定什么呢?他的增加改变了高度?

2019-08-09 17:08 2 · 回答

     老师你好,请问什么不对呢?增大,t分布趋近于Z分布,过来说不可以吗?

2019-08-09 05:05 1 · 回答