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梦梦 · 2024年11月09日

二项分布和贝努利分布的区别

NO.PZ2023091601000028

问题如下:

A fixed income portfolio manager currently holds a portfolio of bonds of various companies. Assuming all these bonds have the same annualized probability of default and that the defaults are independent, the number of defaults in this portfolio over the next year follows which type of distribution?

选项:

A.

Bernoulli

B.

Normal

C.

Binomial

D.

Exponential

解释:

The result would follow a Binomial distribution as there is a fixed number of random variables, each with the same annualized probability of default. It is not a Bernoulli distribution, as a Bernoulli distribution would describe the likelihood of default of one of the individual bonds rather than of the entire portfolio (i.e. a Binomial distribution essentially describes a group of Bernoulli distributed variables). A normal distribution is used to model continuous variables, while in this case the number of defaults within the portfolio is discrete.

老师,第一句和第二句解释二项分布和贝奴利分布的英文能都翻译一下呢?

1 个答案
已采纳答案

pzqa27 · 2024年11月11日

嗨,从没放弃的小努力你好:


这个结果将遵循二项分布,因为随机变量的个数是固定的,每个变量的年化违约概率相同。

这不是伯努利分布,因为伯努利分布描述的是单个债券违约的可能性,而不是整个投资组合违约的可能性(即二项分布本质上描述的是一组伯努利分布变量)。

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

梦梦 · 2024年11月12日

好的,谢谢