pbinom with size argument 0 (PR#8560)
On Sun, 5 Feb 2006, Peter Dalgaard wrote:
P Ehlers <ehlers at math.ucalgary.ca> writes:
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.
What's the problem ?? An n=0 binomial is the sum of an empty set of Bernoulli RV's, and the sum over an empty set is identically 0.
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.
Consistency is what you gain. E.g. binom(.,n=n1+n2,p) == binom(.,n=n1,p) * binom(.,n=n2,p) where * denotes convolution. This will also hold for n1=0 or n2=0 if the binomial in that case is defined as a one-point distribution at zero. Same thing as any(logical(0)) etc., really.
Consistency is a Good Thing, and I had already altered the codebase to consistently allow size=0 as a discrete distribution concentrated at 0. There were other inconsistencies, e.g. whether the geometric/negative binomial functions allow prob=0 or prob=1. I have no problem with prob=1 (it is a discrete distribution concentrated on one point) and this was addressed for rnbinom before (PR#1218) but subsequently broken (which is why we like regression tests ...). However prob=0 does not correspond to a proper distribution unless Inf is allowed as a value, and it was not so documented (nor implemented). Indeed we had
dgeom(2, prob=0)
[1] 0
dgeom(Inf, prob=0)
[1] 0
pgeom(Inf, prob=0)
[1] 0 and in fact dgeom gave zero for every allowed value. So I cannot accept that as being right (and we even have a d-p-q-r test with prob=0).
Brian D. Ripley, ripley at stats.ox.ac.uk Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ University of Oxford, Tel: +44 1865 272861 (self) 1 South Parks Road, +44 1865 272866 (PA) Oxford OX1 3TG, UK Fax: +44 1865 272595