From p.dalgaard at biostat.ku.dk  Sun Feb  5 01:33:31 2006
From: p.dalgaard at biostat.ku.dk (p.dalgaard@biostat.ku.dk)
Date: Sun,  5 Feb 2006 01:33:31 +0100 (CET)
Subject: [Rd] pbinom with size argument 0 (PR#8560)
Message-ID: <20060205003331.A5F6B33585@slim.kubism.ku.dk>

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             ?ster Farimagsgade 5, Entr.B
  c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
 (*) \(*) -- University of Copenhagen   Denmark          Ph:  (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)                  FAX: (+45) 35327907



[Rd] pbinom with size argument 0 (PR#8560)
p.dalgaard@biostat.ku.dk