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From Mikkel Meyer Andersen <m...@mikl.dk>
Subject Re: [math] meaning of "support" in distributions classes
Date Mon, 03 Jan 2011 19:00:50 GMT
2011/1/3 Phil Steitz <phil.steitz@gmail.com>:
> On Mon, Jan 3, 2011 at 1:41 PM, Mikkel Meyer Andersen <mikl@mikl.dk> wrote:
>
>> 2011/1/3 Phil Steitz <phil.steitz@gmail.com>:
>> > On Mon, Jan 3, 2011 at 2:23 AM, Mikkel Meyer Andersen <mikl@mikl.dk>
>> wrote:
>> >
>> >> Hi,
>> >>
>> >> You're right, Phil. Support for beta is [0, 1] and not (0, 1) as stated
>> on
>> >> Wikipedia. As you mention, support for continuous distributions is
>> closed,
>> >> hence the corresponding isInclusive-functions can be discussed. I
>> thought
>> >> about it being useful for infinity, but we could let users deal with
>> this
>> >> themselves?
>> >>
>> >
>> > Yeah, sorry I missed this before.  It hit me when I was  working on the
>> 2_X
>> > retrofit and it looked like Beta was wrong (I see now Wikipedia seems to
>> be
>> > using some other definition - or is just wrong).  I dropped the
>> > inclusive/exclusive functions there.  I think in the discrete case, this
>> can
>> > be handled by convention and the only issue there is the same as the
>> > continuous one - infinities - but these are all the same.  So I propose
>> that
>> > we drop these functions in 3.0 as well.  The isSupportConnected property
>> > still logically makes sense; though it is always true for the 2_X
>> > distributions, so I dropped it there.
>> +1
>> I agree. For now we don't need them, neither in 2.2 nor 3.0. Is there
>> any sense in keeping them if we later on includes distributions where
>> it would be beneficial to have such functions, or should we simply
>> just add them then?
>> >
>>
> I am happy to keep them if I can get a clear understanding of what they
> mean.  As I said in the original post, I think I must be missing something
> that makes them meaningful.  If you use the definition that I gave of
> support, other than infinities, the endpoints are always going to be
> included.  Could well be I am missing something.
No, I don't think that you've missed anything. I probably haven't
given it a decent thought when I included them to begin with. So the
right think is to remove those functions following the de facto
definition of support.

Cheers, Mikkel.
>
> Phil
>
>
>> > Phil
>> >
>> >>
>> >> Cheers, Mikkel.
>> >> Den 02/01/2011 23.05 skrev "Phil Steitz" <phil.steitz@gmail.com>:
>> >> > We don't precisely define what we mean by the support of a
>> distribution
>> >> > anywhere. I have been assuming that we mean the smallest closed set
>> such
>> >> > that its complement has probability 0. This would make, for example,
>> the
>> >> > support of the Beta distribution [0, 1] independent of the parameters.
>> >> But
>> >> > then isSupportLowerBoundInclusive currently returns false for Beta.
I
>> >> must
>> >> > have one of the concepts wrong. Could it be that the
>> >> > upper/lowerboundInclusive attributes are only meaningful in the
>> discrete
>> >> > case?
>> >> >
>> >> > Phil
>> >>
>> >
>>
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>

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