From: P Ehlers <ehlers_at_math.ucalgary.ca>

Date: Sat 04 Feb 2006 - 22:04:58 GMT

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

*>>
*

*>>
*

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

*>>>
*

*>>>>Full_Name: Uffe Høgsbro 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...
*

>>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) ).
*

>>>(But it depends on your point of view, as above ... However,

*>>>surely the two should be consistent with each other.)
*

https://stat.ethz.ch/mailman/listinfo/r-devel Received on Sun Feb 05 09:19:10 2006

Date: Sat 04 Feb 2006 - 22:04:58 GMT

(Ted Harding) wrote:

> On 03-Feb-06 Peter Dalgaard wrote: >

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

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

>>I think Uffe is perfectly right: The result of zero experiments will

> > > 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,

> > > Ted.

I prefer a (consistent) NaN. What happens to our notion of a Binomial RV as a sequence of Bernoulli RVs if we permit n=0? I have never seen (nor contemplated, I confess) the definition of a Bernoulli RV as anything other than some dichotomous-outcome one-trial random experiment. Not n trials, where n might equal zero, but _one_ trial. I can't see what would be gained by permitting a zero-trial experiment. If we assign probability 1 to each outcome, we have a problem with the sum of the probabilities.

Peter Ehlers

> > -------------------------------------------------------------------- > E-Mail: (Ted Harding) <Ted.Harding@nessie.mcc.ac.uk> > Fax-to-email: +44 (0)870 094 0861 > Date: 03-Feb-06 Time: 15:07:49 > ------------------------------ XFMail ------------------------------ > > ______________________________________________ > R-devel@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-devel ______________________________________________R-devel@r-project.org mailing list

https://stat.ethz.ch/mailman/listinfo/r-devel Received on Sun Feb 05 09:19:10 2006

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