## Poisson distribution

Probability function of the Poisson distribution with mean $\mu$ is as follows.

$p(x)=\frac{1}{x!}e^{-\mu} \mu^x (x=0,1,2,…)$

The method using the relationship between the exponential distribution is as follows. $x$ is the maximum of $n$ in the following equation after generating standard uniform random number $U_1,U_2,\cdots$

$U_1 U_2 \cdots U_n>e^{-\frac1\mu }$

If the standard uniform random numbers may take 0, the following formula should be adopted.

$\left(1-U_1\right) \left(1-U_2\right) \cdots \left(1-U_n\right)>e^{{-\frac1\mu }}$

Reference:
• JIS Z 9031:2012, Procedure for random number generation and randomization

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