question: PoissonNextSend not poisson distribution? #23347

If this is a known quirk of Bitcoin's networking code, please feel free to close and I'm sorry for the spam.

From wikipedia a poisson distribution has mean = λ and variance = λ (so std dev = sqrt(λ)). I ran PoissonNextSend 10000 times in a unit test and calculated the mean and std dev of the returned result. I received a mean of λ and a std dev of λ each time. So when passing in 30s, the mean was 30s and the std dev was 30s (and I did remember to take the square root here!). My calculations of the unscaled variable give a mean & std. dev of 1. I was wondering if this is intentional since the "textbook definition" means this is not a poisson distribution.

The time between events is indeed not Poisson distributed, but a Negative Exponential Distribution.

The name comes from the fact that the resulting generated events mimick what is called a Poisson process. The number of events per time unit is however Poisson distributed.

I have a branch here: https://github.com/jnewbery/bitcoin/tree/2021-12-rename-poisson that renames the Poisson* functions, expands the comments, and moves them to more appropriate translation units. Let me know if you think that's an improvement and I can open a PR.