(Ted Harding) wrote: > On 03-Feb-06 Peter Dalgaard wrote: > >>(Ted Harding) <[EMAIL PROTECTED]> writes: >> >> >>>On 03-Feb-06 [EMAIL PROTECTED] 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... > > > 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.
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) <[EMAIL PROTECTED]> > 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
