Generating a quasi Poisson distribution, version 2
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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
- the size,
- the probability,
- the mean,
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.
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