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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 05:26:31 GMT
On Sun, Jan 2, 2011 at 11:46 PM, Ted Dunning <ted.dunning@gmail.com> wrote:

> On Sun, Jan 2, 2011 at 2:05 PM, Phil Steitz <phil.steitz@gmail.com> wrote:
>
> > 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.
>
>
> Why closed?
>
> Why not just the smallest set such that the complement has probability 0?
>

Because that in general will not be well-defined.  Consider, for example,
the support of the Beta distribution.  The smallest closed set whose
complement has probability 0 is [0, 1] (independently of the parameters).
If the definition does not require that the set be closed, then when you
consider (0, 1], [0, 1), [0, 1] - {x} for any x in [0,1],  or [0, 1] minus
any finite number of points...you see that there will be no unique smallest
(in terms of inclusion) set whose complement has probability 0.

Phil

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