Statistics and distribution order
(A) setting
(
X-
. 1
,
X-
2
,
...
,
X-
n-
)
is drawn from the overall
X-
~
F.
(
X
)
of the
sample, they are arranged in ascending order of
X-
(. 1)
≤
X-
(2)
≤
...
≤
X-
(
n-
)
, called
X-
(. 1)
,
X-
(2)
,
...
,
X-
(
n-
)
by sample
X-
. 1
,
X-
2
,
...
,
X-
n-
green
into
order statistics
,
X-
(
k
)
,
referred to as
the first
k
th order statistics
.
The maximum order statistic
X-
(
n-
)
= max {
X-
. 1
,
X-
2
,
...
,
X-
n-
}
Minimum order statistic
X-
(. 1)
= min {
X-
. 1
,
X-
2
,
...
,
X-
n-
}
Range
R & lt
n-
= X-
(
n-
)
-
X-
(. 1)
Example
:
Observations
90,55,80,95,100
sorted
55,80,90,95,100
Observations
80,90,69,80,90
sorted
69,80,80,90,90
Order statistics distribution function
Overall provided
X
distribution function is
F. (
X
)
, the minimum order statistic
X
(. 1)
and the
maximum order statistic
X
(
n-
)
distribution functions are:
The overall probability density function statistics for continuous order
Provided the overall
X
probability density function
F
(
X
)
, the minimum order statistic X (1)
and the maximum order statistic
X
(
n-
)
a probability density function are as follows:
