# lnpdfmvt¶

## Purpose¶

Computes multivariate Student’s t log-probabilities.

## Format¶

z = lnpdfmvt(x, corr, df)
Parameters
• x (NxK matrix) – values at which to evaluate the multivariate Student’s t log-probabilities.

• corr (KxK matrix) – correlation matrix.

• df (scalar) – degrees of freedom.

Returns

z (Nx1 vector) – log-probabilities.

## Examples¶

### Uncorrelated variables¶

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

// Degrees of freedom
df = 5;

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

t = lnpdfmvt(x, corr, df);

print "t =";
t;

t =    -7.17907
-6.80693
-6.42082
-6.02085
-5.60755
-5.18217
-4.74697
-4.30564
-3.86388
-3.42999
-3.01553
-2.63564
-2.30874
-2.05500
-1.89343


### Example 2¶

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

// Degrees of freedom
df = 5;

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

t = lnpdfmvt(x, corr, df);

print "t =";
t;


After the above code:

t =   -5.74003
-5.41290
-5.07813
-4.73673
-4.39021
-4.04075
-3.69138
-3.34617
-3.01045
-2.69093
-2.39574
-2.13420
-1.91636
-1.75201
-1.64956


## Source¶

lnpdfn.src

Functions lnpdft()