[R] Geometric Distribution at prob=c(0,1)

[Thomas Lumley]

On Fri, 12 May 2000, Kjetil Kjernsmo wrote:

> Dear all,
> 
> I'm working with the geometric distribution for the time being, and I'm
> confused. This may have more to do with statistics than R itself, but
> since I'm getting results from R I find counterintuitive (well, yeah, my
> statistical intuition has not been properly sharpened), I feel like
> asking.
> 
> The point first:
> If I do
> > rgeom(1,prob=1)
> I get:
> [1] NaN
> Warning message: 
> NAs produced in: rgeom(n, prob) 
> And if I do:
> > rgeom(1,prob=0)
> I get:
> [1] NaN
> Warning message: 
> NAs produced in: rgeom(n, prob) 
> 
> I was expecting to get 0 and Inf respectively.... Should I expect that?

Yes, and probably No.

As far as I know, none of the rxxx functions produce Inf results -- we
have stuck to real-valued random variables.

We don't have entirely consistent handling of limiting behaviour in
mathematical functions. That is, if a quantity is undefined at a
particular parameter value but has a unique limit we often but not always
provide that limit.

I think rgeom(prob=1) is a case where there is a clearly right answer: 0.
Given that we have recently got upset at the glibc maintainers for not
providing correct limiting behaviour for exp, we should probably fix it.

On the other hand rgeom(prob=0)=Inf is less clearly correct. In the
development version we give NA rather than NaN: that is "we're not going
to answer this" rather than "the answer is undefined".


	-thomas



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