From: Ted Harding <Ted.Harding_at_nessie.mcc.ac.uk>

Date: Fri 03 Feb 2006 - 15:07:52 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,
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*>> since the answer must then be 1 and a lot of computation would
*

*>> be saved (likewise returning 0 when x < 0). However, it would
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*>> 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.
*

E-Mail: (Ted Harding) <Ted.Harding@nessie.mcc.ac.uk> Fax-to-email: +44 (0)870 094 0861

https://stat.ethz.ch/mailman/listinfo/r-devel Received on Sat Feb 04 02:13:46 2006

Date: Fri 03 Feb 2006 - 15:07:52 GMT

On 03-Feb-06 Peter Dalgaard wrote:

> (Ted Harding) <Ted.Harding@nessie.mcc.ac.uk> writes: >

>> On 03-Feb-06 uht@dfu.min.dk wrote:

> > Once you get your coffee, you'll likely realize that you got > your p's and d's mixed up...

You're right about the mix-up! (I must mend the pipeline.)

> I think Uffe is perfectly right: The result of zero experiments will > be zero successes (and zero failures) with probability 1, so the > cumulative distribution function is a step function with one step at > zero ( == as.numeric(x>=0) ).

I'm perfectly happy with this argument so long as it leads to dbinom(x=0,size=0,prob=p)=1 and also pbinom(q=0,size=0,prob=p)=1 (which seems to be what you are arguing too). And I think there are no traps if p=0 or p=1.

>> (But it depends on your point of view, as above ... However,

*>> surely the two should be consistent with each other.)
*

Ted.

E-Mail: (Ted Harding) <Ted.Harding@nessie.mcc.ac.uk> Fax-to-email: +44 (0)870 094 0861

Date: 03-Feb-06 Time: 15:07:49 ------------------------------ XFMail ------------------------------ ______________________________________________R-devel@r-project.org mailing list

https://stat.ethz.ch/mailman/listinfo/r-devel Received on Sat Feb 04 02:13:46 2006

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