<s>
Inverse	B-Algorithm
transform	I-Algorithm
sampling	I-Algorithm
(	O
also	O
known	O
as	O
inversion	B-Algorithm
sampling	I-Algorithm
,	O
the	O
inverse	O
probability	O
integral	O
transform	O
,	O
the	O
inverse	O
transformation	O
method	O
,	O
Smirnov	O
transform	O
,	O
or	O
the	O
golden	O
rule	O
)	O
is	O
a	O
basic	O
method	O
for	O
pseudo-random	B-Algorithm
number	I-Algorithm
sampling	I-Algorithm
,	O
i.e.	O
,	O
for	O
generating	O
sample	O
numbers	O
at	O
random	O
from	O
any	O
probability	O
distribution	O
given	O
its	O
cumulative	O
distribution	O
function	O
.	O
</s>
<s>
As	O
a	O
result	O
,	O
this	O
method	O
may	O
be	O
computationally	O
inefficient	O
for	O
many	O
distributions	O
and	O
other	O
methods	O
are	O
preferred	O
;	O
however	O
,	O
it	O
is	O
a	O
useful	O
method	O
for	O
building	O
more	O
generally	O
applicable	O
samplers	O
such	O
as	O
those	O
based	O
on	O
rejection	B-Algorithm
sampling	I-Algorithm
.	O
</s>
<s>
the	O
Box	B-Algorithm
–	I-Algorithm
Muller	I-Algorithm
transform	I-Algorithm
)	O
may	O
be	O
preferred	O
computationally	O
.	O
</s>
<s>
It	O
is	O
often	O
the	O
case	O
that	O
,	O
even	O
for	O
simple	O
distributions	O
,	O
the	O
inverse	B-Algorithm
transform	I-Algorithm
sampling	I-Algorithm
method	I-Algorithm
can	O
be	O
improved	O
on	O
:	O
see	O
,	O
for	O
example	O
,	O
the	O
ziggurat	B-Algorithm
algorithm	I-Algorithm
and	O
rejection	B-Algorithm
sampling	I-Algorithm
.	O
</s>
<s>
On	O
the	O
other	O
hand	O
,	O
it	O
is	O
possible	O
to	O
approximate	O
the	O
quantile	O
function	O
of	O
the	O
normal	O
distribution	O
extremely	O
accurately	O
using	O
moderate-degree	O
polynomials	O
,	O
and	O
in	O
fact	O
the	O
method	O
of	O
doing	O
this	O
is	O
fast	O
enough	O
that	O
inversion	B-Algorithm
sampling	I-Algorithm
is	O
now	O
the	O
default	O
method	O
for	O
sampling	O
from	O
a	O
normal	O
distribution	O
in	O
the	O
statistical	O
package	O
R	B-Language
.	O
</s>
<s>
The	O
problem	O
that	O
the	O
inverse	B-Algorithm
transform	I-Algorithm
sampling	I-Algorithm
method	I-Algorithm
solves	O
is	O
as	O
follows	O
:	O
</s>
<s>
The	O
inverse	B-Algorithm
transform	I-Algorithm
sampling	I-Algorithm
method	I-Algorithm
works	O
as	O
follows	O
:	O
</s>
<s>
Generate	B-Algorithm
a	I-Algorithm
random	I-Algorithm
number	I-Algorithm
from	O
the	O
standard	O
uniform	O
distribution	O
in	O
the	O
interval	O
,	O
i.e.	O
</s>
<s>
Inverse	B-Algorithm
transform	I-Algorithm
sampling	I-Algorithm
can	O
be	O
simply	O
extended	O
to	O
cases	O
of	O
truncated	O
distributions	O
on	O
the	O
interval	O
without	O
the	O
cost	O
of	O
rejection	B-Algorithm
sampling	I-Algorithm
:	O
the	O
same	O
algorithm	O
can	O
be	O
followed	O
,	O
but	O
instead	O
of	O
generating	O
a	O
random	O
number	O
uniformly	O
distributed	O
between	O
0	O
and	O
1	O
,	O
generate	O
uniformly	O
distributed	O
between	O
and	O
,	O
and	O
then	O
again	O
take	O
.	O
</s>
