[Rd] pbinom with size argument 0 (PR#8560)
p.dalgaard at biostat.ku.dk
Sun Feb 5 01:33:05 CET 2006
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.
O__ ---- Peter Dalgaard Øster Farimagsgade 5, Entr.B
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