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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 19:16:56 GMT
2011/1/3 Phil Steitz <phil.steitz@gmail.com>:
> 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.
+1
>
> 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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