In this article "generate quasi-poisson distribution random variables", it is shown how to use the function
rnbinom to simulate overdispersed Poisson data:
rqpois <- function(n, mu, theta) rnbinom(n=n, mu=mu, size=mu/(theta-1)).
rqpois works well but it is clearly undefined for values of
theta less than one. As such, it can only simulate overdispersed data. And it is unclear to me how to modify the function to simulate under-dispersed data.
The empirical context is a series of (iid) competitions where I expect people to see what the others are doing and decide whether to enter or stay out. The count of entrants is what I am interested in. Empirically I found the data are "underdispersed" (i.e., mean >> var).