<s>
The	O
Cornish	B-General_Concept
–	I-General_Concept
Fisher	I-General_Concept
expansion	I-General_Concept
is	O
an	O
asymptotic	O
expansion	O
used	O
to	O
approximate	O
the	O
quantiles	O
of	O
a	O
probability	O
distribution	O
based	O
on	O
its	O
cumulants	O
.	O
</s>
<s>
The	O
values	O
γ1	O
and	O
γ2	O
are	O
the	O
random	O
variable	O
's	O
skewness	B-General_Concept
and	O
(	O
excess	O
)	O
kurtosis	B-Error_Name
respectively	O
.	O
</s>
<s>
The	O
value(s )	O
in	O
each	O
set	O
of	O
brackets	O
are	O
the	O
terms	O
for	O
that	O
level	O
of	O
polynomial	O
estimation	O
,	O
and	O
all	O
must	O
be	O
calculated	O
and	O
combined	O
for	O
the	O
Cornish	B-General_Concept
–	I-General_Concept
Fisher	I-General_Concept
expansion	I-General_Concept
at	O
that	O
level	O
to	O
be	O
valid	O
.	O
</s>
<s>
Let	O
X	O
be	O
a	O
random	O
variable	O
with	O
mean	O
10	O
,	O
variance	O
25	O
,	O
skew	O
5	O
,	O
and	O
excess	O
kurtosis	B-Error_Name
of	O
2	O
.	O
</s>
<s>
We	O
can	O
use	O
the	O
first	O
two	O
bracketed	O
terms	O
above	O
,	O
which	O
depend	O
only	O
on	O
skew	O
and	O
kurtosis	B-Error_Name
,	O
to	O
estimate	O
quantiles	O
of	O
this	O
random	O
variable	O
.	O
</s>
<s>
For	O
comparison	O
,	O
the	O
95th	O
percentile	O
of	O
a	O
normal	O
random	O
variable	O
with	O
mean	O
10	O
and	O
variance	O
25	O
would	O
be	O
about	O
18.224	O
;	O
it	O
makes	O
sense	O
that	O
the	O
normal	O
random	O
variable	O
has	O
a	O
lower	O
95th	O
percentile	O
value	O
,	O
as	O
the	O
normal	O
distribution	O
has	O
no	O
skew	O
or	O
excess	O
kurtosis	B-Error_Name
,	O
and	O
so	O
has	O
a	O
thinner	O
tail	O
than	O
the	O
random	O
variableX	O
.	O
</s>
