Poisson Distribution vs Binomial Distribution

最新推荐文章于 2025-05-20 02:33:42 发布

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本文探讨了在Binomial Distribution中当n非常大且p非常小时，该事件可以被视为Poisson Distribution的情况。通过将p设置为λ/n，可以得到Poisson Distribution的结果。文中还提供了一个实验结论，即在实际世界中的Binomial分布中，当n大于等于20且p小于等于0.05时，可以视为Poisson Distribution。

As it says if the "n" is very large andoppositely the "p" very small in a Binomial Distribution event, we can see this event as a Poisson Distribution.

At first, I have been confused. Why?

Google it and the wikipedia webside( to open a foreign web side is very hard and slow or even "404 Error" in formal way ). Got it.

If you make the "p" as "λ/n", you would get the result as "Poisson Distribution".

We would like to use this conclusion:

Following is the "greating" process:

Proving Process 【1】

It is so great.

Therehas aconclusion from those experiments: if the n>=20 or upper and the p<=0.05 or lower in thereal world's Binomial distribution, we can see it as Poisson Distribution--X~P(np).