# Convert a beta distribution to Poisson distribution

I need a Poisson distribution in an application, but in that application the only available functions for generating distributions are Beta, Uniform, and Normal functions. Now, I am thinking is there a way I could draw a beta distribution, but change the parameters in a way so as to approximate a Poisson distribution? Thanks.

• Since a Beta(1,1) is a Uniform(0,1), you can code any generic Poisson random generator using that Beta generator. Or you can use the connection between Poisson and Exponential, plus the fact that a $\chi^2_2$ is an Exponential $\cal{E}(1/2)$. – Xi'an Apr 4 '18 at 7:37

## 1 Answer

Answer from comments: Since a beta(1,1) distribution is uniform(0,1), you can just use that to code a standard poisson variable generator. Some algorithms are given here: https://en.wikipedia.org/wiki/Poisson_distribution#Generating_Poisson-distributed_random_variables.

Or you can use the connection between Poisson and Exponential, plus the fact that a $\chi^2_2$ is an Exponential $\cal{E}(1/2)$.