<s>
In	O
statistics	O
,	O
the	O
Lilliefors	B-General_Concept
test	I-General_Concept
is	O
a	O
normality	B-General_Concept
test	I-General_Concept
based	O
on	O
the	O
Kolmogorov	B-General_Concept
–	I-General_Concept
Smirnov	I-General_Concept
test	I-General_Concept
.	O
</s>
<s>
It	O
is	O
used	O
to	O
test	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
that	O
data	O
come	O
from	O
a	O
normally	O
distributed	O
population	O
,	O
when	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
does	O
not	O
specify	O
which	O
normal	O
distribution	O
;	O
i.e.	O
,	O
it	O
does	O
not	O
specify	O
the	O
expected	O
value	O
and	O
variance	O
of	O
the	O
distribution	O
.	O
</s>
<s>
A	O
variant	O
of	O
the	O
test	O
can	O
be	O
used	O
to	O
test	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
that	O
data	O
come	O
from	O
an	O
exponentially	O
distributed	O
population	O
,	O
when	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
does	O
not	O
specify	O
which	O
exponential	O
distribution	O
.	O
</s>
<s>
Then	O
find	O
the	O
maximum	O
discrepancy	O
between	O
the	O
empirical	B-General_Concept
distribution	I-General_Concept
function	I-General_Concept
and	O
the	O
cumulative	O
distribution	O
function	O
(	O
CDF	O
)	O
of	O
the	O
normal	O
distribution	O
with	O
the	O
estimated	O
mean	O
and	O
estimated	O
variance	O
.	O
</s>
<s>
Finally	O
,	O
assess	O
whether	O
the	O
maximum	O
discrepancy	O
is	O
large	O
enough	O
to	O
be	O
statistically	B-General_Concept
significant	I-General_Concept
,	O
thus	O
requiring	O
rejection	O
of	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
Since	O
the	O
hypothesised	O
CDF	O
has	O
been	O
moved	O
closer	O
to	O
the	O
data	O
by	O
estimation	O
based	O
on	O
those	O
data	O
,	O
the	O
maximum	O
discrepancy	O
has	O
been	O
made	O
smaller	O
than	O
it	O
would	O
have	O
been	O
if	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
had	O
singled	O
out	O
just	O
one	O
normal	O
distribution	O
.	O
</s>
<s>
its	O
probability	O
distribution	O
assuming	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
true	O
,	O
is	O
stochastically	O
smaller	O
than	O
the	O
KolmogorovSmirnov	O
distribution	O
.	O
</s>
<s>
This	O
is	O
the	O
Lilliefors	B-General_Concept
distribution	I-General_Concept
.	O
</s>
<s>
To	O
date	O
,	O
tables	O
for	O
this	O
distribution	O
have	O
been	O
computed	O
only	O
by	O
Monte	B-Algorithm
Carlo	I-Algorithm
methods	I-Algorithm
.	O
</s>
