On Sun, 5 Feb 2006, Peter Dalgaard wrote: > P Ehlers <[EMAIL PROTECTED]> 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, [EMAIL PROTECTED] 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 ______________________________________________ R-devel@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-devel
