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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).

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You can sample from a discrete distribution, the Poisson sounds like a good fit here.

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  • $\begingroup$ Poisson looks like it would be perfect here, but if OP didn't like the mean = variance aspect, they could also sample from a negative binomial distribution, which is similar but doesn't require that restriction. $\endgroup$
    – Noah
    Oct 24, 2018 at 15:30
  • $\begingroup$ Thanks both. I'm trying to do this in excel, and I found a nice way to do this using inverse binomial here - reddit.com/r/excel/comments/3hsdyg/… $\endgroup$
    – dashnick
    Oct 24, 2018 at 15:31

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