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
