<s>
The	O
Box	B-Algorithm
–	I-Algorithm
Muller	I-Algorithm
transform	I-Algorithm
,	O
by	O
George	O
Edward	O
Pelham	O
Box	O
and	O
Mervin	O
Edgar	O
Muller	O
,	O
is	O
a	O
random	B-Algorithm
number	I-Algorithm
sampling	I-Algorithm
method	O
for	O
generating	O
pairs	O
of	O
independent	O
,	O
standard	O
,	O
normally	O
distributed	O
(	O
zero	O
expectation	O
,	O
unit	O
variance	O
)	O
random	O
numbers	O
,	O
given	O
a	O
source	O
of	O
uniformly	O
distributed	O
random	O
numbers	O
.	O
</s>
<s>
The	O
Box	B-Algorithm
–	I-Algorithm
Muller	I-Algorithm
transform	I-Algorithm
is	O
commonly	O
expressed	O
in	O
two	O
forms	O
.	O
</s>
<s>
The	O
Box	B-Algorithm
–	I-Algorithm
Muller	I-Algorithm
transform	I-Algorithm
was	O
developed	O
as	O
a	O
more	O
computationally	O
efficient	O
alternative	O
to	O
the	O
inverse	B-Algorithm
transform	I-Algorithm
sampling	I-Algorithm
method	I-Algorithm
.	O
</s>
<s>
The	O
ziggurat	B-Algorithm
algorithm	I-Algorithm
gives	O
a	O
more	O
efficient	O
method	O
for	O
scalar	O
processors	O
(	O
e.g.	O
</s>
<s>
old	O
CPUs	O
)	O
,	O
while	O
the	O
Box	B-Algorithm
–	I-Algorithm
Muller	I-Algorithm
transform	I-Algorithm
is	O
superior	O
for	O
processors	O
with	O
vector	O
units	O
(	O
e.g.	O
</s>
<s>
The	O
polar	O
method	O
differs	O
from	O
the	O
basic	O
method	O
in	O
that	O
it	O
is	O
a	O
type	O
of	O
rejection	B-Algorithm
sampling	I-Algorithm
.	O
</s>
<s>
When	O
and	O
are	O
equal	O
to	O
this	O
the	O
Box	B-Algorithm
–	I-Algorithm
Muller	I-Algorithm
transform	I-Algorithm
produces	O
a	O
normal	O
random	O
deviate	O
equal	O
to	O
.	O
</s>
<s>
The	O
standard	O
Box	B-Algorithm
–	I-Algorithm
Muller	I-Algorithm
transform	I-Algorithm
generates	O
values	O
from	O
the	O
standard	O
normal	O
distribution	O
(	O
i.e.	O
</s>
<s>
The	O
implementation	O
below	O
in	O
standard	O
C++	B-Language
generates	O
values	O
from	O
any	O
normal	O
distribution	O
with	O
mean	O
and	O
variance	O
.	O
</s>
<s>
The	O
random	O
number	O
generator	O
has	O
been	O
seeded	B-Algorithm
to	O
ensure	O
that	O
new	O
,	O
pseudo-random	O
values	O
will	O
be	O
returned	O
from	O
sequential	O
calls	O
to	O
the	O
generateGaussianNoise	O
function	O
.	O
</s>
