Ok. That makes sense.
Sent from my iPhone
On Jan 2, 2011, at 9:26 PM, Phil Steitz <phil.ste...@gmail.com> wrote:
> On Sun, Jan 2, 2011 at 11:46 PM, Ted Dunning <ted.dunn...@gmail.com> wrote:
>
>> On Sun, Jan 2, 2011 at 2:05 PM, Phil Steitz <phil.ste...@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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