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Conditional normal distribution

  1. Oct 22, 2007 #1
    Hi all

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

    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
  2. jcsd
  3. Oct 22, 2007 #2


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    You mean, some of the vector components have positive realizations while some other components have negative realizations, is that correct?
  4. Oct 22, 2007 #3
    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
    Last edited: Oct 22, 2007
  5. Oct 23, 2007 #4


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    Have you thought of applying the Bayes rule?
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