R help - May 2000 - Geometric Distribution at prob=c(0,1)

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?

Going back to my textbooks (Dudewicz and Mishra 1988, primarily), they
describe the geometric dist as the dist of a random variable that gives
the number of the trail that an event occurs, with a constant probability
p (or prob). Contrary to R, my textbooks have x = 1, 2, 3, ... 

My intuition says that with this interpretation, a probability of 0 means
that the event just won''t happen, and consequently rgeom(1,prob=0)
should
always return Inf. qgeom() seems to agree:
> qgeom(1,1)
[1] Inf

rgeom(1,prob=1) says to me that the event must occur on the first trail,
and with x = 0, 1, 2, ..., that means it should return 0. Here,
> qgeom(0,0)
[1] NaN
Warning message: 
NaNs produced in: qgeom(p, prob, lower.tail, log.p) 

Is it my intuition that is playing tricks with me (again), or is it a bug? 
  
Yours Confusedly,

Kjetil
-- 
Kjetil Kjernsmo
Graduate astronomy-student                    Problems worthy of attack
University of Oslo, Norway            Prove their worth by hitting back
E-mail: kjetikj at astro.uio.no                                - Piet Hein
Homepage <URL:http://www.astro.uio.no/~kjetikj/>
Webmaster at skepsis.no 


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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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