Re: Marginals of a trivariate normal
- From: eggstone <zhi.ouyang@xxxxxxxxx>
- Date: Fri, 21 Sep 2007 06:30:11 -0700
On Sep 20, 4:34 pm, paleostat <paleol...@xxxxxxxxx> wrote:
I am trying to get clarity on the following problem, which was posed
to me by a friend (who claims to be the orignal formulator!). It's
very simple to state, but I am stuck. The answer is not known to me.
Here it is:
"Consider three random variables, X, Y, Z. we assume that each pair of
random variables follows a bivariate normal distribution. Is this
sufficient to state that the joint distribution of the three random
variables is normal?"
It is well known that normal marginals of a bivariate distribution
don't imply a joint normal. the previous question is to some extent a
generalization of this statement in higher dimensions.
Any insight is greatly appreciated!
-G
No, I won't think so. Although the counter example would not be
obvious to
construct. But I am sure you can make one by Copula methods.
Zhi
.
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