# Generating a quasi Poisson distribution, version 2

[This article was first published on

Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

**Freakonometrics - Tag - R-english**, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

Here and there, I mentioned two codes to generated quasiPoisson random variables. And in both of them, the negative binomial approximation seems to be wrong. Recall that the negative binomial distribution is

whereand in R, a negative binomial distribution can be parametrized using two parameters, out of the following ones

- the size,
- the probability,
- the mean,

Here, we consider a distribution such that and . In the previous posts, I used

rqpois = function(n, lambda, phi) { mu = lambda k = mu/(phi * mu - 1) r1 = rnbinom(n, mu = mu, size = k) r2 = rnbinom(n, size=phi*mu/(phi-1),prob=1/phi) k = mu/phi/(1-1/phi) r3 = rnbinom(n, mu = mu, size = k) r4 = rnbinom(n, size=mu/phi/(1-1/phi),prob=1/phi) r = cbind(r1,r2,r3,r4) return(r) }

> N=rqpois(1000000,2,4) > mean(N[,1]) [1] 2.001992 > mean(N[,2]) [1] 8.000033 > var(N[,1])/ mean(N[,1]) [1] 7.97444 > var(N[,2])/ mean(N[,2]) [1] 4.002022

> mean(N[,3]) [1] 2.001667 > mean(N[,4]) [1] 2.002776 > var(N[,3])/ mean(N[,3]) [1] 3.999318 > var(N[,4])/ mean(N[,4]) [1] 4.009647So, finally it is better when we do the maths well.

To

**leave a comment**for the author, please follow the link and comment on their blog:**Freakonometrics - Tag - R-english**.R-bloggers.com offers

**daily e-mail updates**about R news and tutorials about learning R and many other topics. Click here if you're looking to post or find an R/data-science job.

Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.