Re: [Rd] pbinom with size argument 0 (PR#8560)

From: Ted Harding <Ted.Harding_at_nessie.mcc.ac.uk>
Date: Fri 03 Feb 2006 - 14:34:32 GMT

On 03-Feb-06 uht@dfu.min.dk wrote:
> Full_Name: Uffe Høgsbro Thygesen
> Version: 2.2.0
> OS: linux
> Submission from: (NULL) (130.226.135.250)
>
>
> Hello all.
>
> pbinom(q=0,size=0,prob=0.5)
>
> returns the value NaN. I had expected the result 1. In fact any
> value for q seems to give an NaN.

Well, "NaN" can make sense since "q=0" refers to a single sampled value, and there is no value which you can sample from "size=0"; i.e. sampling from "size=0" is a non-event. I think the probability of a non-event should be NaN, not 1! (But maybe others might argue that if you try to sample from an empty urn you necessarily get zero "successes", so p should be 1; but I would counter that you also necessarily get zero "failures" so q should be 1. I suppose it may be a matter of whether you regard the "r" of the binomial distribution as referring to the "identities" of the outcomes rather than to how many you get of a particular type. Hmmm.)

> Note that
>
> dbinom(x=0,size=0,prob=0.5)
>
> returns the value 1.

That is probably because the .Internal code for pbinom may do a preliminary test for "x >= size". This also makes sense, for the cumulative p<dist> for any <dist> with a finite range, since the answer must then be 1 and a lot of computation would be saved (likewise returning 0 when x < 0). However, it would make even more sense to have a preceding test for "size<=0" and return NaN in that case since, for the same reasons as above, the result is the probability of a non-event.

Best wishes,
Ted.

E-Mail: (Ted Harding) <Ted.Harding@nessie.mcc.ac.uk> Fax-to-email: +44 (0)870 094 0861
Date: 03-Feb-06                                       Time: 14:34:28
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