# [R] Goodness of fit to Poisson / NegBinomial

Mark Myatt mark at myatt.demon.co.uk
Thu Feb 8 15:31:32 CET 2001

```Yudi,

Thanks for this:

>x_ c(70, 38, 17, 10,  9, 6)
>kk_ 0:5
>n_ sum(x)
>
>fn_ function(p){
>    r_ p[1]
>    th_ p[2]
>    ll _ -sum(x[1:max(kk)]*log(dnbinom(kk[-length(kk)],r,th))) -
>          x[length(kk)]*log(1-pnbinom((max(kk)-1),r,th))
>    return(ll)
>}
>
>a_ nlm(fn,p=c(.9,.5),hes=T)
>est_ a\$est
>
>phat_ c(dnbinom(kk[-length(kk)],est[1],est[2]),
>        1-pnbinom((max(kk)-1),est[1],est[2]))
>E_ n*phat
>chi2_ sum((x-E)^2/E)
>cat('Chi2 goodness-of-fit = ',chi2,'\n')
>cat('P-value=',1-pchisq(chi2,df=length(kk)-1-2),'\n')
>
>print(cbind(O=x,E=round(E,1),err=round((x-E)^2/E,1)))

It is certainly more elegant than anything I would have come up with but
I just cannot get it to work (Rwin 1.21). The call to nlm() returns:

Warning messages:
1: NA/Inf replaced by maximum positive value
2: NA/Inf replaced by maximum positive value
3: NA/Inf replaced by maximum positive value
4: NA/Inf replaced by maximum positive value
5: NA/Inf replaced by maximum positive value
6: NA/Inf replaced by maximum positive value
7: NA/Inf replaced by maximum positive value
8: NA/Inf replaced by maximum positive value

est holds the starting parameters:

[1] 0.9 0.5

E (from n*phat) holds:

[1] 80.38301  0.00000  0.00000  0.00000  0.00000  3.90972

which gives a very big chi-square.

Sorry to be a nuisance.

Mark

--
Mark Myatt

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```