<s>
In	O
probability	O
theory	O
,	O
a	O
Pitman	B-General_Concept
–	I-General_Concept
Yor	I-General_Concept
process	I-General_Concept
denoted	O
PY(d,θ,G0 )	O
,	O
is	O
a	O
stochastic	O
process	O
whose	O
sample	O
path	O
is	O
a	O
probability	O
distribution	O
.	O
</s>
<s>
When	O
d	O
=	O
0	O
,	O
it	O
becomes	O
the	O
Dirichlet	B-General_Concept
process	I-General_Concept
.	O
</s>
<s>
The	O
discount	O
parameter	O
gives	O
the	O
PitmanYor	O
process	O
more	O
flexibility	O
over	O
tail	O
behavior	O
than	O
the	O
Dirichlet	B-General_Concept
process	I-General_Concept
,	O
which	O
has	O
exponential	O
tails	O
.	O
</s>
<s>
The	O
exchangeable	O
random	O
partition	O
induced	O
by	O
the	O
Pitman	B-General_Concept
–	I-General_Concept
Yor	I-General_Concept
process	I-General_Concept
is	O
an	O
example	O
of	O
a	O
Poisson	O
–	O
Kingman	O
partition	O
,	O
and	O
of	O
a	O
Gibbs	O
type	O
random	O
partition	O
.	O
</s>
<s>
The	O
name	O
"	O
Pitman	B-General_Concept
–	I-General_Concept
Yor	I-General_Concept
process	I-General_Concept
"	O
was	O
coined	O
by	O
Ishwaran	O
and	O
James	O
after	O
Pitman	O
and	O
Yor	O
's	O
review	O
on	O
the	O
subject	O
.	O
</s>
<s>
It	O
is	O
also	O
sometimes	O
referred	O
to	O
as	O
the	O
two-parameter	O
Poisson	O
–	O
Dirichlet	B-General_Concept
process	I-General_Concept
,	O
after	O
the	O
two-parameter	O
generalization	O
of	O
the	O
Poisson	O
–	O
Dirichlet	O
distribution	O
which	O
describes	O
the	O
joint	O
distribution	O
of	O
the	O
sizes	O
of	O
the	O
atoms	O
in	O
the	O
random	O
measure	O
,	O
sorted	O
by	O
strictly	O
decreasing	O
order	O
.	O
</s>
