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