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Date: Mon, 3 Jan 2011 14:15:29 -0500
Message-ID: <AANLkTim3QzShBpfHMP3GCsAprZn+_qJU7OVtVfMUbf0w@mail.gmail.com>
Subject: Re: [math] meaning of "support" in distributions classes
From: Phil Steitz <phil.steitz@gmail.com>
To: Commons Developers List <dev@commons.apache.org>
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On Mon, Jan 3, 2011 at 2:04 PM, Ted Dunning <ted.dunning@gmail.com> wrote:

> I don't think you are missing anything.  Moreover, I think that wikipedia
> just has an error in this regard.
>
> Following their chain of definitions leads to this example:
>
>
> http://en.wikipedia.org/wiki/Support_(measure_theory)#A_uniform_distribution<http://en.wikipedia.org/wiki/Support_%28measure_theory%29#A_uniform_distribution>
>
> If the uniform distribution on the open interval (0,1) has the closed set
> [0,1] as its support then the beta distribution
> obviously does as well.  In fact, the definition they use starts with "The
> largest closed set ...".
>
> Yes.  We should probably state somewhere in the javadoc that we are using
that definition.  A possible modification that would make the Wikipedia Beta
example make sense (but make the Uniform example wrong ;) would be to
consider whether or not the endpoints are in the domain of the density
function.  I don't see that info as adding a lot of value, so am +1 for just
dropping the isXxxIncluded properties, but leaving isSupportConnected in
place.

Phil


> On Mon, Jan 3, 2011 at 11:00 AM, Mikkel Meyer Andersen <mikl@mikl.dk>
> wrote:
>
> > > 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.
> >
>

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