Looking at a graph of a poisson distribution, it starts low, peaks, then falls off. That's not the right distribution to use here. We need to start high, and fall off. The peak should be the very first sample.

If you are using a difficulty such that you have a 50% chance of getting a share each hash, the distribution will look like so:
1st hash: 50%
2nd hash: 25%
3rd hash: 12.5%
4th hash: 6.25%
and so on, dividing by two each time.

So whatever kind of distribution you call that.