# lnpdfmvn¶

## Purpose¶

Computes multivariate Normal log-probabilities.

## Format¶

z = lnpdfmvn(x, corr)
Parameters:
• x (NxK matrix) – values at which to evaluate the multivariate normal log probabilities.

• corr (KxK matrix) – correlation matrix.

Returns:

z (Nx1 vector) – log-probabilities.

## Examples¶

### Uncorrelated variables¶

// Correlation matrix
corr = { 1 0 , 0 1 };

// X values
x1 = seqa(-3, .2, 3/.2);
x2 = seqa(-3, .2, 3/.2);
x = x1~x2;

z = lnpdfmvn(x, corr);

print "z =";
z;

z =    -10.83788
-9.67788
-8.59788
-7.59788
-6.67788
-5.83788
-5.07788
-4.39788
-3.79788
-3.27788
-2.83788
-2.47788
-2.19788
-1.99788
-1.87788


### Example 2¶

// Correlation matrix
corr = { 1 0.60 , 0.60 1 };

// X values
x1 = seqa(-3, .2, 3/.2);
x2 = seqa(-3, .2, 3/.2);
x = x1~x2;

z = lnpdfmvn(x, corr);

print "z =";
z;


After the above code:

z =     -7.23973
-6.51473
-5.83973
-5.21473
-4.63973
-4.11473
-3.63973
-3.21473
-2.83973
-2.51473
-2.23973
-2.01473
-1.83973
-1.71473
-1.63973


## Remarks¶

This computes the multivariate Normal log-probability for each row of x.

lnpdfn.src