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wgl · 2024年06月25日

plugging in 那一行里的计算是什么意思?

NO.PZ2020010303000013

问题如下:

If the kurtosis of some returns on a small-cap stock portfolio was 6, what would the degrees of freedom parameter be if they were generated by a generalized Student’s tυt_\upsilon? What if the kurtosis was 9?

选项:

解释:

In a Student’s t, the kurtosis depends only on the degree of freedom and is k = 3(v-2)/( v-4).

This can be solved so that k(v - 4) = 3(v - 2) so that kv - 4k = 3v - 6 and kv - 3v = 4k - 6.

Finally, solving for v, v =(4k-6)/ (k-3)

Plugging in v =(24-6)/(6-3)=18/3=6 and v =(36-6)/ (9-3)= 5.

The degree of freedom is v-1.

The kurtosis falls rapidly as v grows.

For example, if v = 12 then k = 3.75, which is only slightly higher than the kurtosis of a normal (3).

plugging in 那一行里的计算是什么意思?

1 个答案

pzqa39 · 2024年06月26日

嗨,努力学习的PZer你好:


这一行就是代数,分别把6和9代进上一步得出来的等式计算即可。


这道题在基础班“Mixture Distribution”有讲过,可以看一下。


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