<s>
Its	O
cumulative	O
distribution	O
function	O
is	O
the	O
logistic	O
function	O
,	O
which	O
appears	O
in	O
logistic	O
regression	O
and	O
feedforward	B-Algorithm
neural	I-Algorithm
networks	I-Algorithm
.	O
</s>
<s>
It	O
resembles	O
the	O
normal	O
distribution	O
in	O
shape	O
but	O
has	O
heavier	O
tails	O
(	O
higher	O
kurtosis	B-Error_Name
)	O
.	O
</s>
<s>
In	O
this	O
equation	O
is	O
the	O
mean	O
,	O
and	O
is	O
a	O
scale	O
parameter	O
proportional	O
to	O
the	O
standard	B-General_Concept
deviation	I-General_Concept
.	O
</s>
<s>
An	O
alternative	O
parameterization	O
of	O
the	O
logistic	O
distribution	O
can	O
be	O
derived	O
by	O
expressing	O
the	O
scale	O
parameter	O
,	O
,	O
in	O
terms	O
of	O
the	O
standard	B-General_Concept
deviation	I-General_Concept
,	O
,	O
using	O
the	O
substitution	O
,	O
where	O
.	O
</s>
<s>
The	O
logistic	O
distribution	O
—	O
and	O
the	O
S-shaped	B-Algorithm
pattern	O
of	O
its	O
cumulative	O
distribution	O
function	O
(	O
the	O
logistic	O
function	O
)	O
and	O
quantile	O
function	O
(	O
the	O
logit	O
function	O
)	O
—	O
have	O
been	O
extensively	O
used	O
in	O
many	O
different	O
areas	O
.	O
</s>
<s>
One	O
of	O
the	O
most	O
common	O
applications	O
is	O
in	O
logistic	O
regression	O
,	O
which	O
is	O
used	O
for	O
modeling	O
categorical	O
dependent	O
variables	O
(	O
e.g.	O
,	O
yes-no	O
choices	O
or	O
a	O
choice	O
of	O
3	O
or	O
4	O
possibilities	O
)	O
,	O
much	O
as	O
standard	O
linear	B-General_Concept
regression	I-General_Concept
is	O
used	O
for	O
modeling	O
continuous	O
variables	O
(	O
e.g.	O
,	O
income	O
or	O
population	O
)	O
.	O
</s>
<s>
Specifically	O
,	O
logistic	O
regression	O
models	O
can	O
be	O
phrased	O
as	O
latent	O
variable	O
models	O
with	O
error	B-General_Concept
variables	I-General_Concept
following	O
a	O
logistic	O
distribution	O
.	O
</s>
<s>
This	O
phrasing	O
is	O
common	O
in	O
the	O
theory	O
of	O
discrete	O
choice	O
models	O
,	O
where	O
the	O
logistic	O
distribution	O
plays	O
the	O
same	O
role	O
in	O
logistic	O
regression	O
as	O
the	O
normal	O
distribution	O
does	O
in	O
probit	B-Architecture
regression	I-Architecture
.	O
</s>
