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小壹万万呀 · 2022年01月22日

可以解释一下C选项吗

NO.PZ2018122701000030

问题如下:

Let X be a random variable representing the daily loss of your portfolio. The "peaks over threshold" (POT) approach considers a threshold value, u, of X and the distribution of excess losses over this threshold. Which of the following statements about this application of extreme value theory is correct?

选项:

A.

To apply the POT approach, the distribution of X must be elliptical and known.

B.

If X is normally distributed, the distribution of excess losses requires the estimation of only one parameter, β, which is a positive scale parameter.

C.

To apply the POT approach, one must choose a threshold, u, which is high enough that the number of observations in excess of u is zero.

D.

As the threshold, u, increases, the distribution of excess losses over u converges to a generalized Pareto distribution.

解释:

D is correct.

考点: Extreme Value

解析: The distribution of excess losses over u converges to a generalized Pareto distribution as the threshold value u increases.

The distribution of X itself can be any of the commonly used distribution: normal, lognormal, t, etc., and will usually be known. The distribution of excess losses requires the estimation of two parameters, a positive scale parameter β and a shape or tail index parameter ξ. One must choose a threshold u that is high enough so that the theory applies but also low enough so that there are observations in excess of u.

可以解释一下C选项吗

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已采纳答案

李坏_品职助教 · 2022年01月22日

嗨,爱思考的PZer你好:


C说的是POT方法需要选择一个阈值U,这个U必须足够高,使得超过阈值U的观测值数量为0.


可以看一下讲义P44,C说法是错误的,应该是U应该足够低,使得有足够的观测值超过u才对。

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2023-01-18 23:42 1 · 回答

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2022-03-13 17:03 2 · 回答

NO.PZ2018122701000030

2021-08-07 21:51 1 · 回答

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2021-01-18 20:43 2 · 回答