Conditional normal distribution

[jstar]

Hi all

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

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 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?

thanks for all input, J

 

[EnumaElish]

the vector x has to groups of variables, those that I know are below zero (x_bz), and those that I know are above zero (x_az).

You mean, some of the vector components have positive realizations while some other components have negative realizations, is that correct?

 

[jstar]

yes, I do know the signs and would like to know how the positive vector components are distributed conditional on the information that the others are below zero (but I do not know what value they hold - only the signs).

so what I want is to condition the multivariate normal distribution on an intervall - and not as usually on a single value or vector:

p(x_az|x_bz<0) <> p(x_az|x_bz=0).

and then truncate the resulting distribution above zero (which should be the easier part, I think/hope)

thank for any idea

 

[EnumaElish]

Have you thought of applying the Bayes rule?