update on dnbinom with large "size"

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~  turns out I don't need to look at the C code.

~  if one uses the mu/size parameterization of the
negative binomial, R computes size/(size+mu) to
switch parameterizations.  If size>>mu this
gets rounded to 1 ... should be easy enough
to test and return NA under these circumstances?
It is all vectorized, so not so easy.  But why is NA appropriate, when a 
Poisson approximation seems more appropriate?

The same issue affects [pqr]nbinom, of course.

The short-term advice is of course 'don't do that' but use a suitable 
approximation such as Poisson.  Maybe there are reasons to support values 
of size > 1e10, but I suspect only for completeness and maybe it is better 
to at least give a warning.
function (x, size, prob, mu, log = FALSE)
{
~    if (!missing(mu)) {
~        if (!missing(prob))
~            stop("'prob' and 'mu' both specified")
~        prob <- size/(size + mu)
~    }
~    .Internal(dnbinom(x, size, prob, log))
}

~  Ben Bolker

- --------------------------
~  Check it out:

curve(dnbinom(1,mu=0.5,size=x),log="x",from=1,to=1e18)
abline(h=dpois(1,lambda=0.5),col=2,lty=2)
text(1,dpois(1,lambda=0.5)+0.02,"Poisson",col=2,pos=4)

~  I will take a look in the C code when I get
a chance to see if I can offer
a patch, but in the meantime wanted to alert people to
this "feature" ...  (it looks like I will have to go
through dnbinom and dbinom_raw to see where the problem
is ...)

~   Ben Bolker

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Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
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update on dnbinom with large "size"

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