Bilingual edition: English is preserved and Chinese follows each unit. Terminology uses the confirmed v20260916 glossary; automated semantic review remains traceable.
中英双语版：英文原文完整保留，中文紧随对应单元；术语采用 v20260916 确认表，自动语义审校结果可追溯。

Comparison of Distribution Functions

分布函数比较
Distribution
分布
Functional Form
函数形式
Mean
平均
Standard Deviation
标准差

Binomial

二项式

Gaussian

高斯

Poisson

泊松
If the probability of an event is p = and there are n = events, then the probability of that event being observed is:
Distribution
分布
Value of x
x的值
Probability
概率
Binomial
二项式
 x 10^
Gaussian
高斯
 x 10^
Poisson
泊松
 x 10^
For these conditions, the mean number of events is and the standard deviation is .

Note!

注意！
The binomial distribution is the exact probability, so the above comparison can serve to check on the conditions under which the Gaussian and Poisson distributions are good approximations to it. If you substitute numbers, you will find that the Poisson is a good approximation if the probability p is small and the number of events n is large. If the number of events is large and the probability is also sizable, then the Gaussian will be a better approximation.
如果事件的概率是 p = ，共有 n = 个事件，那么该事件被观测到的概率为：在这些条件下，平均事件数为 ，标准差为 。二项分布是精确的概率，因此上述比较可以用来检验高斯分布和泊松分布在什么条件下能作为它的良好近似。如果你代入数值，会发现当概率 p 很小且事件数 n 很大时，泊松分布是一个良好的近似。如果事件数很大且概率也较大，那么高斯分布会是更好的近似。
中文译文中的待填/计算数值依次对应：1：p 2：n 3：x 4：probb 5：probp 6：xg 7：probbg 8：probpg 9：xp 10：probbp 11：probpp 12：mean 13：sdev。实际数值以上方原输入框为准。
 Index

Distribution functions
索引分布函数
 
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