<s>
In	O
statistics	O
,	O
the	O
matrix	B-General_Concept
t-distribution	I-General_Concept
(	O
or	O
matrix	B-Architecture
variate	O
t-distribution	O
)	O
is	O
the	O
generalization	O
of	O
the	O
multivariate	B-General_Concept
t-distribution	I-General_Concept
from	O
vectors	O
to	O
matrices	B-Architecture
.	O
</s>
<s>
The	O
matrix	B-General_Concept
t-distribution	I-General_Concept
shares	O
the	O
same	O
relationship	O
with	O
the	O
multivariate	B-General_Concept
t-distribution	I-General_Concept
that	O
the	O
matrix	B-Architecture
normal	O
distribution	O
shares	O
with	O
the	O
multivariate	O
normal	O
distribution	O
.	O
</s>
<s>
For	O
example	O
,	O
the	O
matrix	B-General_Concept
t-distribution	I-General_Concept
is	O
the	O
compound	O
distribution	O
that	O
results	O
from	O
sampling	O
from	O
a	O
matrix	B-Architecture
normal	O
distribution	O
having	O
sampled	O
the	O
covariance	O
matrix	B-Architecture
of	O
the	O
matrix	B-Architecture
normal	O
from	O
an	O
inverse	O
Wishart	O
distribution	O
.	O
</s>
<s>
In	O
a	O
Bayesian	B-General_Concept
analysis	I-General_Concept
of	O
a	O
multivariate	O
linear	O
regression	O
model	O
based	O
on	O
the	O
matrix	B-Architecture
normal	O
distribution	O
,	O
the	O
matrix	B-General_Concept
t-distribution	I-General_Concept
is	O
the	O
posterior	O
predictive	O
distribution	O
.	O
</s>
<s>
The	O
characteristic	O
function	O
and	O
various	O
other	O
properties	O
can	O
be	O
derived	O
from	O
the	O
generalized	O
matrix	B-General_Concept
t-distribution	I-General_Concept
(	O
see	O
below	O
)	O
.	O
</s>
<s>
The	O
generalized	O
matrix	B-General_Concept
t-distribution	I-General_Concept
is	O
a	O
generalization	O
of	O
the	O
matrix	B-General_Concept
t-distribution	I-General_Concept
with	O
two	O
parameters	O
α	O
and	O
β	O
in	O
place	O
of	O
ν	O
.	O
</s>
<s>
The	O
generalized	O
matrix	B-General_Concept
t-distribution	I-General_Concept
is	O
the	O
compound	O
distribution	O
that	O
results	O
from	O
an	O
infinite	O
mixture	O
of	O
a	O
matrix	B-Architecture
normal	O
distribution	O
with	O
an	O
inverse	O
multivariate	O
gamma	O
distribution	O
placed	O
over	O
either	O
of	O
its	O
covariance	O
matrices	B-Architecture
.	O
</s>
<s>
and	O
where	O
is	O
the	O
type-two	O
Bessel	O
function	O
of	O
Herz	O
of	O
a	O
matrix	B-Architecture
argument	O
.	O
</s>
