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. -------------------------------------------------------------------- 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
