pbinom with size argument 0 (PR#8560)

On 03-Feb-06 Peter Dalgaard wrote:

(Ted Harding) <Ted.Harding at nessie.mcc.ac.uk> writes:

On 03-Feb-06 uht at dfu.min.dk wrote:

Full_Name: Uffe H?gsbro Thygesen
Version: 2.2.0
OS: linux
Submission from: (NULL) (130.226.135.250)


Hello all.

 pbinom(q=0,size=0,prob=0.5)

returns the value NaN. I had expected the result 1. In fact any
value for q seems to give an NaN.

Well, "NaN" can make sense since "q=0" refers to a single sampled
value, and there is no value which you can sample from "size=0";
i.e. sampling from "size=0" is a non-event. I think the probability
of a non-event should be NaN, not 1! (But maybe others might argue
that if you try to sample from an empty urn you necessarily get
zero "successes", so p should be 1; but I would counter that you
also necessarily get zero "failures" so q should be 1. I suppose
it may be a matter of whether you regard the "r" of the binomial
distribution as referring to the "identities" of the outcomes
rather than to how many you get of a particular type. Hmmm.)

Note that

 dbinom(x=0,size=0,prob=0.5)

returns the value 1.

That is probably because the .Internal code for pbinom may do
a preliminary test for "x >= size". This also makes sense, for
the cumulative p<dist> for any <dist> with a finite range,
since the answer must then be 1 and a lot of computation would
be saved (likewise returning 0 when x < 0). However, it would
make even more sense to have a preceding test for "size<=0"
and return NaN in that case since, for the same reasons as
above, the result is the probability of a non-event.

Once you get your coffee, you'll likely realize that you got
your p's and d's mixed up...

You're right about the mix-up! (I must mend the pipeline.)

I think Uffe is perfectly right: The result of zero experiments will
be zero successes (and zero failures) with probability 1, so the
cumulative distribution function is a step function with one step at
zero ( == as.numeric(x>=0) ).

I'm perfectly happy with this argument so long as it leads to
dbinom(x=0,size=0,prob=p)=1 and also pbinom(q=0,size=0,prob=p)=1
(which seems to be what you are arguing too). And I think there
are no traps if p=0 or p=1.

(But it depends on your point of view, as above ... However,
surely the two  should be consistent with each other.)

Ted.

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Date: 03-Feb-06                                       Time: 15:07:49
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