I have a data set that I’d expect to follow a Poisson distribution, but it is overdispersed by about 3-fold. At the present, I’m modelling this overdispersion using something like the following code in R.

`## assuming a median value of 1500 med = 1500 rawdist = rpois(1000000,med) oDdist = rawDist + ((rawDist-med)*3)`

Visually, this seems to fit my empirical data very well. If I’m happy with the fit, is there any reason that I should be doing something more complex, like using a negative binomial distribution, as described here? (If so, any pointers or links on doing so would be much appreciated).

Oh, and I’m aware that this creates a slightly jagged distribution (due to the multiplication by three), but that shouldn’t matter for my application.

Update:For the sake of anyone else who searches and finds this question, here’s a simple R function to model an overdispersed poisson using a negative binomial distribution. Set d to the desired mean/variance ratio:`rpois.od<-function (n, lambda,d=1) { if (d==1) rpois(n, lambda) else rnbinom(n, size=(lambda/(d-1)), mu=lambda) }`

(via the R mailing list: https://stat.ethz.ch/pipermail/r-help/2002-June/022425.html)

**Answer**

for overdispersed poisson, use the negative binomial, which allows you to parameterize the variance as a function of the mean precisely. rnbinom(), etc. in R.

**Attribution***Source : Link , Question Author : chrisamiller , Answer Author : Cyrus S*