Language Reference
RANDNORMAL Function
RANDNORMAL (N, Mean, Cov ) ;
This function is supported by the IML procedure and the iml action.
The RANDNORMAL function is part of the IMLMLIB library. The RANDNORMAL function returns an 
matrix that contains N random draws from the multivariate normal distribution with mean vector Mean and covariance matrix Cov.
The inputs are as follows:
- N
is the number of desired observations sampled from the multivariate normal distribution.
- Mean
is a
vector of means. - Cov
is a
symmetric positive definite variance-covariance matrix.
If X follows a multivariate normal distribution with mean vector 
and variance-covariance matrix 
, then
-
the probability density function for x is
if
, the probability density function reduces to a univariate normal distribution. the expected value of
is 
. the covariance of
and 
is 
.
The following example generates 1,000 samples from a two-dimensional multivariate normal distribution with mean vector (1, 2) and a given covariance matrix. Each row of the returned matrix x is a row vector sampled from the multivariate normal distribution. The example computes the sample mean and covariance and compares them with the expected values.
call randseed(1);
N = 1000;
Mean = {1 2};
Cov = {2.4 3, 3 8.1};
x = RandNormal( N, Mean, Cov );
SampleMean = mean(x);
SampleCov = cov(x);
print SampleMean Mean, SampleCov Cov;
Figure 344: Estimated Mean and Covariance Matrix
| SampleMean | Mean | ||
|---|---|---|---|
| 1.0619604 | 2.1156084 | 1 | 2 |
| SampleCov | Cov | ||
|---|---|---|---|
| 2.5513518 | 3.2729559 | 2.4 | 3 |
| 3.2729559 | 8.7099585 | 3 | 8.1 |
For further details about sampling from the multivariate normal distribution, see Gentle (2003).