Hello all A pragmatic argument for allowing size==0 is the situation where the size is in itself a random variable (that's how I stumbled over the inconsistency, by the way). For example, in textbooks on probability it is stated that: If X is Poisson(lambda), and the conditional distribution of Y given X is Binomial(X,p), then Y is Poisson(lambda*p). (cf eg Pitman's "Probability", p. 400) Clearly this statement requires Binomial(0,p) to be a well-defined distribution. Such statements would be quite convoluted if we did not define Binomial(0,p) as a legal (but degenerate) distribution. The same applies to codes where the size parameter may attain the value 0. Just my 2 cents. Cheers, Uffe -----Oprindelig meddelelse----- Fra: pd at pubhealth.ku.dk p? vegne af Peter Dalgaard Sendt: s? 05-02-2006 01:33 Til: P Ehlers Cc: ted.harding at nessie.mcc.ac.uk; Peter Dalgaard; R-bugs at biostat.ku.dk; r-devel at stat.math.ethz.ch; Uffe H?gsbro Thygesen Emne: Re: [Rd] pbinom with size argument 0 (PR#8560) 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