25008 - Generate data from a multivariate normal distribution

Sample 25008: Generate data from a multivariate normal distribution

Generate data from a multivariate normal distribution

Contents:

Purpose / Requirements / Usage / Limitations

NOTE: The MVN macro is obsolete. Beginning in SAS 9.2, use the RANDNORMAL function in SAS/IML software or PROC SIMNORMAL in SAS/STAT software to generate multivariate normal data.

PURPOSE:

The %MVN macro generates multivariate normal data using the Cholesky root of the variance-covariance matrix. Bivariate normal data can be generated using the DATA step.

REQUIREMENTS:

Version 6 or later of SAS/IML software. The DATA step code for generating bivariate normal data requires only Version 6 Base SAS software.

USAGE:

Follow the instructions in the Downloads tab of this sample to save the %MVN macro definition. Replace the text within quotes in the following statement with the location of the %MVN macro definition file on your system. In your SAS program or in the SAS editor window, specify this statement to define the %MVN macro and make it available for use:

   %inc "<location of your file containing the MVN macro>";

Following this statement, you may call the %MVN macro. See the Results tab for an example.

The following parameters are required except for SEED=:

VARCOV=

SAS data set that contains the variance-covariance (and only the variance covariance) matrix. The macro expects m variables and m observations in the data set, where m is the number of variables to generate.

MEANS=

SAS data set that contains the mean vector. The macro expects a single variable with m observations containing the m means for the variables generated.

N=

Number of observations to generate.

SEED=

Starting seed value for the random number generator. Default value is 0, which will use the system clock to generate a seed.

SAMPLE=

SAS data set name for the resulting multivariate normal data. The variable names will be COL1-COLm.

LIMITATIONS:

No error checking is done. The macro assumes that dataset names entered are valid, and exist in the case of the VARCOV= and MEANS= options.

These sample files and code examples are provided by SAS Institute Inc. "as is" without warranty of any kind, either express or implied, including but not limited to the implied warranties of merchantability and fitness for a particular purpose. Recipients acknowledge and agree that SAS Institute shall not be liable for any damages whatsoever arising out of their use of this material. In addition, SAS Institute will provide no support for the materials contained herein.

Generating bivariate normal data using the DATA step

Three methods are presented in increasing order of efficiency. In each case, the desired means (MU1 and MU2), variances (VAR1 and VAR2), and correlation coefficient (RHO) are specified. PROC CORR verifies that the generated data have the desired distribution.


data a;
  keep x y;
  mu1=10; mu2=20; var1=4; var2=9; rho=.5;
  do i = 1 to 10000;
    x = mu1+sqrt(var1)*rannor(123);
    y = (mu2+rho*(sqrt(var2)/sqrt(var1))*(x-mu1)) +
        sqrt(var2*(1-rho**2))*rannor(123);
      output;
  end;
run;
proc corr noprob; run;


data b;
  keep x y;
  mu1=10; mu2=20; var1=4; var2=9; rho=.5;
  do i = 1 to 10000;
     /*  generate standard normal variates with corr of rho  */
     x = rannor(123);
     y = rho*x+sqrt(1-rho**2)*rannor(123);

     /*  transform to designated mean and variance  */
     x = mu1 + sqrt(var1)*x;
     y = mu2 + sqrt(var2)*y;
       output;
  end;
run;
proc corr noprob; run;


data c;
  keep x y;
  mu1=10; mu2=20; var1=4; var2=9; rho=.5;
  std1=sqrt(var1);  std2=sqrt(var2);
  c=sqrt(1-rho**2);
    do i = 1 to 10000;
       x = rannor(123);
       y = rho*x+c*rannor(123);
       x = mu1 + sqrt(var1)*x;
       y = mu2 + sqrt(var2)*y;
         output;
    end;
run;
proc corr noprob; run;

These sample files and code examples are provided by SAS Institute Inc. "as is" without warranty of any kind, either express or implied, including but not limited to the implied warranties of merchantability and fitness for a particular purpose. Recipients acknowledge and agree that SAS Institute shall not be liable for any damages whatsoever arising out of their use of this material. In addition, SAS Institute will provide no support for the materials contained herein.

Date Modified:	2016-06-01 15:36:02
Date Created:	2005-01-13 15:03:27

Product Family	Product	Host	SAS Release
Product Family	Product	Host	Starting	Ending
SAS System	SAS/STAT	All	n/a	n/a
SAS System	SAS/IML	All	n/a	n/a

Support

Sample 25008: Generate data from a multivariate normal distribution

Generate data from a multivariate normal distribution

Generating bivariate normal data using the DATA step

Operating System and Release Information