Fluorite | Level 6

## Generating multivariate data with various distributions in SAS/IML

Hi everyone,

I would like to know if there is a way to generate multiple variables where each has a certain distributional form given a covariance matrix. Specifically, I'm looking to generate three variables (X1, X2, X3) with X1~lognormal, X2~multimodal and a X3~normal distribution, and also allow for correlation among all three (given a covariance matrix).

I read about generating univariate data from each type of distribution independently and also ways to generate MVN or more complex distributions given a covariance matrix, but I can't seem to find a way to allow for different distributional forms given a covariance matrix.

highly appreciate any help.

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Accepted Solutions
SAS Super FREQ

## Re: Generating multivariate data with various distributions in SAS/IML

The technique you are looking for is called a "copula." It is a multivariate distribution with a given correlation structure with specified marginal distributions for each variable.  You can use PROC COPULA in SAS if you have a SAS/ETS license. Chapter 9 of Simulating Data with SAS (Wicklin, 2013) includes SAS/IML programs that generate correlated variables for discrete variables (binary and ordinal) as well as the copula approach for continuous variables (pp. 164-170). I also describe a powerful technique called the Iman-Conover method (pp. 161-164).

2 REPLIES 2
SAS Super FREQ

## Re: Generating multivariate data with various distributions in SAS/IML

The technique you are looking for is called a "copula." It is a multivariate distribution with a given correlation structure with specified marginal distributions for each variable.  You can use PROC COPULA in SAS if you have a SAS/ETS license. Chapter 9 of Simulating Data with SAS (Wicklin, 2013) includes SAS/IML programs that generate correlated variables for discrete variables (binary and ordinal) as well as the copula approach for continuous variables (pp. 164-170). I also describe a powerful technique called the Iman-Conover method (pp. 161-164).

Fluorite | Level 6

## Re: Generating multivariate data with various distributions in SAS/IML

Many thanks for your help. Got the book and the programs and everything works well.
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