Hello all A pragmatic argument for allowing size=3D=3D0 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=20 distribution of Y given X is Binomial(X,p), then=20 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: [EMAIL PROTECTED] p=E5 vegne af Peter Dalgaard Sendt: s=F8 05-02-2006 01:33 Til: P Ehlers Cc: [EMAIL PROTECTED]; Peter Dalgaard; [EMAIL PROTECTED]; = r-devel@stat.math.ethz.ch; Uffe H=F8gsbro Thygesen Emne: Re: [Rd] pbinom with size argument 0 (PR#8560) =20 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=3D0? > 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.=20 What's the problem ?? An n=3D0 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.=20 binom(.,n=3Dn1+n2,p) =3D=3D binom(.,n=3Dn1,p) * binom(.,n=3Dn2,p) where * denotes convolution. This will also hold for n1=3D0 or n2=3D0 if the binomial in that case is defined as a one-point distribution at zero. Same thing as any(logical(0)) etc., really. --=20 O__ ---- Peter Dalgaard =D8ster Farimagsgade 5, Entr.B c/ /'_ --- Dept. of Biostatistics PO Box 2099, 1014 Cph. K (*) \(*) -- University of Copenhagen Denmark Ph: (+45) = 35327918 ~~~~~~~~~~ - ([EMAIL PROTECTED]) FAX: (+45) = 35327907 ______________________________________________ R-devel@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-devel
