<s>
In	O
probability	O
theory	O
and	O
statistics	O
,	O
the	O
Dirichlet	B-General_Concept
negative	I-General_Concept
multinomial	I-General_Concept
distribution	I-General_Concept
is	O
a	O
multivariate	O
distribution	O
on	O
the	O
non-negative	O
integers	O
.	O
</s>
<s>
It	O
is	O
also	O
a	O
generalization	O
of	O
the	O
negative	B-General_Concept
multinomial	I-General_Concept
distribution	I-General_Concept
(NM(k , p )	O
)	O
allowing	O
for	O
heterogeneity	O
or	O
overdispersion	O
to	O
the	O
probability	O
vector	O
.	O
</s>
<s>
then	O
the	O
marginal	O
distribution	O
of	O
X	O
is	O
a	O
Dirichlet	B-General_Concept
negative	I-General_Concept
multinomial	I-General_Concept
distribution	I-General_Concept
:	O
</s>
<s>
In	O
the	O
above	O
,	O
is	O
the	O
negative	B-General_Concept
multinomial	I-General_Concept
distribution	I-General_Concept
and	O
is	O
the	O
Dirichlet	O
distribution	O
.	O
</s>
<s>
The	O
Dirichlet	O
distribution	O
is	O
a	O
conjugate	O
distribution	O
to	O
the	O
negative	B-General_Concept
multinomial	I-General_Concept
distribution	I-General_Concept
.	O
</s>
<s>
For	O
a	O
random	B-General_Concept
vector	I-General_Concept
of	O
category	O
counts	O
,	O
distributed	O
according	O
to	O
a	O
negative	B-General_Concept
multinomial	I-General_Concept
distribution	I-General_Concept
,	O
the	O
compound	O
distribution	O
is	O
obtained	O
by	O
integrating	O
on	O
the	O
distribution	O
for	O
p	O
which	O
can	O
be	O
thought	O
of	O
as	O
a	O
random	B-General_Concept
vector	I-General_Concept
following	O
a	O
Dirichlet	O
distribution	O
:	O
</s>
<s>
The	O
conditional	O
distribution	O
of	O
a	O
Dirichlet	B-General_Concept
negative	I-General_Concept
multinomial	I-General_Concept
distribution	I-General_Concept
on	O
is	O
Dirichlet-multinomial	O
distribution	O
with	O
parameters	O
and	O
.	O
</s>
<s>
The	O
random	B-General_Concept
vector	I-General_Concept
of	O
observed	O
draws	O
of	O
the	O
other	O
non-red	O
colors	O
are	O
distributed	O
according	O
to	O
a	O
.	O
</s>
