I am trying to create some simulated data, where for each participant, the average number of events that occur in a given week can be any positive number, but usually in the range of 0 to 5. Trouble is, a lot of the time the average is small, like 0.25. I can only sample whole numbers, i.e. 0, 1, 2, 3, 4, 5. How do I sample from these distributions and still maintain their distribution average over all weeks?
(If the averages were all between 0 and 1, and those were my only options, I would just sample a random number between 0 and 1 and return a 1 if it was less than the average).