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From Phil Steitz <phil.ste...@gmail.com>
Subject Re: [math] meaning of "support" in distributions classes
Date Mon, 03 Jan 2011 18:50:45 GMT
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.

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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