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st: RE: Multivariate "mixed" distribution

From   "Haas, Roy W" <[email protected]>
To   <[email protected]>
Subject   st: RE: Multivariate "mixed" distribution
Date   Mon, 1 Nov 2004 11:26:52 -0600

You can always use the following two-step process. Let X be the (standard) normal variable that you want to change the marginal distribution of. Then U=F(X), where F() is the standard normal cdf, has a uniform distribution. Then Y=G*(U) has the cumulative distribution G(), where G* is the inverse function of G. You may have to approximate the covariance between Y and the other marginals by a series expansion or similar device, but you now have the desired marginal distribution.

Roy W. Haas, Ph.D.
Department of Medicine
UT Health Science Center at San Antonio
7703 Floyd Curl Drive
San Antonio, TX 78229-3900
(210) 567-9272

-----Original Message-----
From: [email protected]
[mailto:[email protected]]On Behalf Of n p
Sent: Monday, November 01, 2004 11:16 AM
To: [email protected]
Subject: st: Multivariate "mixed" distribution

Dear statalisters,

I want to simulate five random variables with known
variance-covariance matrix. I know that if the joint
pdf is multivariate normal one can use the drawnorm
command or the "multiplication with the
cholesky(var-cov)" trick as described in Stata's site
FAQs. I have used the same principle to draw samples
from other multivariate distributions e.g.
multivariate t (I think it works there too). I thought
I could do the same with "mixed" multivariate
distributions e.g. normal for the first 4 variables
and some other skewed distribution for the fifth (i.e.
Gumbel) but I am afraid that it doesn't work. 
What i am trying to do is a sensitivity analysis on
violations of the multivariate normality assumption of
some model thus I want to see what's happening when
only one of the five variables is not normal but is
stil correlated with the other four.
I hope that I made it clear. Sorry for the somehow
off-topic question but I think that some knoledgeable
members of the list could help.

Nikos Pantazis

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