commons-dev mailing list archives

Site index · List index
Message view « Date » · « Thread »
Top « Date » · « Thread »
From Ted Dunning <ted.dunn...@gmail.com>
Subject Re: [math] meaning of "support" in distributions classes
Date Mon, 03 Jan 2011 07:03:22 GMT
Ok. That makes sense. 

Sent from my iPhone

On Jan 2, 2011, at 9:26 PM, Phil Steitz <phil.steitz@gmail.com> wrote:

> 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

---------------------------------------------------------------------
To unsubscribe, e-mail: dev-unsubscribe@commons.apache.org
For additional commands, e-mail: dev-help@commons.apache.org


Mime
View raw message