Re: conditional multivariate normal distribution

On Mon, 22 Oct 2007 16:57:00 +0100, "David Jones" <dajxxxx@xxxxxxxxx>
wrote:

jstar wrote:
Hi all

First of all, I am new here but I am not new to statistics. But I
need your help on this one:

I do have a multivariate normal distribution: x~p(mu,sig)

the vector x has to groups of variables, those that I know are below

I'm curious about the language, or notation.

You seem to be saying that certain elements x_i of x are
always less than zero, and other elements are always
greater than zero.

Then you divide the vector x into two parts.
And then, condition by something that is true by definition.
SO, I don't see a question. What am I missing?

zero (x_bz), and those that I know are above zero (x_az).
I am interested in the conditional distribution of the x above zero:
p(x_az|x_bz<0). Can someone help me derive this distribution or is
this a known distribution I was to stupid to find?


It is not something for which there are simple formulae, although there may be something for the 2 variate case. General formulae can be derived by working with the multivariate CDF to get first a conditional multivariate CDF and then the correspnsing density if necessary.

David Jones

David seemed to understand it....

--
Rich Ulrich, wpilib@xxxxxxxx
http://www.pitt.edu/~wpilib/index.html
.

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