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Brian邵彬 · 2024年04月16日

请问这里自由度是n-1,是因为题干中提到是some of the returns么

  1. FRM I
  2. Quantitative

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).

请问这里自由度是n-1,是因为题干中提到是some of the returns么

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1 个答案

品职答疑小助手雍 · 2024年04月17日

同学你好，对的，问到自由度的问题一般都是只样本的分布了，才会有n-1。

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