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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 18:41:19 GMT
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?
>
> 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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