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Roy
science forum addict
Joined: 03 May 2005
Posts: 51
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 Posted: Tue May 03, 2005 7:54 pm Post subject:
what does non-degenerate distribution mean?
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Hi, this might be a stupid question.
What does it mean when we say a random variable has a non-degenerate
distribution ?
Thanks
Roy |
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Alan
science forum addict
Joined: 03 May 2005
Posts: 51
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| Posted: Tue May 03, 2005 9:03 pm Post subject:
Re: what does non-degenerate distribution mean?
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"Roy" <royliuk@hotmail.com> wrote in message
news:1115157281.887020.95900@o13g2000cwo.googlegroups.com...
| Quote: | Hi, this might be a stupid question.
What does it mean when we say a random variable has a non-degenerate
distribution ?
|
Without seeing the context it very likely means: it's not degenerate,
where by a degenerate r.v., call it X, we mean:
X has only a single possible value with probability 1.
Example: X = 5 with probability 1.
If X is normally defined in a continuum of possible states, this degeneracy
is often phrased as the distribution having 'unit mass' at some point in the
state space.
Physics types would say the distribution is a dirac-delta function. |
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Stephen J. Herschkorn
science forum Guru
Joined: 24 Mar 2005
Posts: 641
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| Posted: Wed May 04, 2005 4:18 am Post subject:
Re: what does non-degenerate distribution mean?
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Roy wrote:
| Quote: | What does it mean when we say a random variable has a non-degenerate
distribution ?
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It means that for any number c, P{X = c} < 1 (where X is ths random
variable in question). A degenerate probability distirbution is one
supported by a single point.
--
Stephen J. Herschkorn sjherschko@netscape.net |
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Roy
science forum addict
Joined: 03 May 2005
Posts: 51
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| Posted: Wed May 04, 2005 3:17 pm Post subject:
Re: what does non-degenerate distribution mean?
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Thank you all very much.
I found sth from
http://www.absoluteastronomy.com/encyclopedia/D/De/Degenerate_distribution.htm
about degenerate distribution.
quote begin
"
In Quick Facts about: mathematics
A science (or group of related sciences) dealing with the logic of
quantity and shape and arrangementmathematics, a degenerate
distribution is the Quick Facts about: probability distribution
Quick Summary not found for this subjectprobability distribution of a
random variable which always has the same value. Examples are a
two-headed coin, a die that always comes up six. This doesn't sound
very Quick Facts about: random
Quick Summary not found for this subjectrandom, but it satisfies the
definition of Quick Facts about: random variable
A variable quantity that is randomrandom variable.
The degenerate distribution is localized at a point x in the Quick
Facts about: real line
Quick Summary not found for this subjectreal line. On this page it is
enough to think about the example localized at 0: that is, the unit
measure located at 0.
The Quick Facts about: cumulative distribution function
Quick Summary not found for this subjectcumulative distribution
function of the degenerate distribution is then the Quick Facts about:
Heaviside step function
Quick Summary not found for this subjectHeaviside step function:
"
quote end |
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