st: RE: drawnorm equivalent for different distribution types?

["Feiveson, Alan H. (JSC-SK311)" <alan.h.feiveson@nasa.gov>]

Ariel - If you wanted to generate correlated RV's from a specific continuous distribution you could do this with a copula transformation:

1. Use drawnorm N(0, R) to get X1, x2, etc . where R is a specified correlation matrix.

2. Transform to a "copula" - i.e. dependent uniforms by U1 = normal(X1), U2 = normal(X2), etc.

3. Transform U's to distribution of choice using inverse CDF: Y1 = invcdf(U1), Y2 = invcdf(U2). For example to transform to correlated gammas, use "invcdf()" as  invgammap().

4. The problem is however that the correlations between the Y's will never be as "high" (i.e. in absolute value) as the correlations in R. I believe it can be proved that only if the Ys are multivariate normal, will the correlations come out the same. However you could experiment by making the correlations in R somewhat higher than what you really want so that the correlations of the Y's is approximately what you want.

Al Feiveson




-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Ariel Linden, DrPH
Sent: Sunday, September 01, 2013 3:22 PM
To: statalist@hsphsun2.harvard.edu
Subject: st: drawnorm equivalent for different distribution types?

Hi All,

Is there an equivalent to -drawnorm- for different distribution types? So for example, let's say I wanted two Poisson distributed variables with a correlation of 0.50? Or a chi-sq distribution, etc...

Thanks!

Ariel

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