From: Prof Brian Ripley <ripley_at_stats.ox.ac.uk>

Date: Mon 06 Feb 2006 - 09:51:36 GMT

Date: Mon 06 Feb 2006 - 09:51:36 GMT

On Sun, 5 Feb 2006, Peter Dalgaard wrote:

> P Ehlers <ehlers@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@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 ______________________________________________ R-devel@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-develReceived on Mon Feb 06 21:14:52 2006

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