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.

Source

lnpdfn.src