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cenwandada · 2024年07月11日

这道题可以解释一下吗

NO.PZ2023100703000029

问题如下:

According to extreme value theory (EVT), when examining distributions of losses exceeding a threshold value, which of the following is correct?

选项:

A.To apply EVT, the underlying loss distribution must be either normal or lognormal.

B.The threshold value is typically chosen near the estimated mean of the underlying loss distribution.

C.The number of exceedances decreases as the threshold value decreases, which causes the reliability of the parameter estimates to increase.

D.As the threshold value is increased, the distribution of exceedances converges to a generalized Pareto distribution.

解释:

A key foundation of EVT is than as the threshold value is increased, the distribution of loss exceedances converges to a generalized Pareto distribution. Assuming the threshold is high enough, excess losses can be modeled using the Generalized Pareto distribution. To apply EVT, the underlying loss distribution can be any of the commonly used distributions: normal, lognormal, t, etc., and will usually be unknown. Choosing the threshold value near the estimated mean of the underlying loss distribution is arbitrary and this method is not typically employed. As the threshold value is decreased, the number of exceedances increases.

这道题可以解释一下吗

1 个答案

pzqa39 · 2024年07月13日

嗨,从没放弃的小努力你好:


根据极值理论,当我们研究超出某个阈值的极端损失时,随着这个阈值不断提高,这些超出阈值的损失(即超额损失)的分布会趋向于一种特定的分布,叫做广义帕累托分布。

 

简单来说:在处理极端损失(如自然灾害、金融危机等)时,我们关注的是那些非常大的损失,通过选择一个较高的阈值,只保留超过这个阈值的损失数据,这样的数据代表了极端情况;随着我们选择的阈值越来越高,超过这个阈值的损失数据(超额损失)会逐渐表现出一种特定的统计特性,即它们的分布会收敛于广义帕累托分布。

 

A错误:应用EVT时,损失分布不需要是正态或对数正态分布,可以是任何常见分布。

B错误:阈值通常不会选择在损失分布的均值附近,基础损失分布的均值代表了所有损失的平均水平,不适合作为极端事件的阈值。选择均值附近的阈值会导致我们包含大量非极端损失,这与极值理论研究极端事件的初衷不符。

C错误:随着阈值的降低,超过阈值的次数实际上会增加,而不是减少。

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