Given a sample of minimum
(1)
and maximum
(2)
Important functions of order statistics include the statistical
range
(3)
midrange
(4)
and statistical median
(5)
(Hogg and Craig 1970, p. 152).
If probability density function distribution
function
(6)
for
A robust estimation technique based on linear
combinations of order statistics is called an L-estimate .
See also Extreme Value Distribution ,
Hinge ,
Maximum ,
Midrange ,
Minimum ,
Statistical
Median
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References Balakrishnan, N. and Chen, W. W. S. Handbook of Tables for Order Statistics from Lognormal Distributions with Applications. Balakrishnan, N. and Cohen, A. C.
Order
Statistics and Inference. Balakrishnan,
N. and Rao, C. R. (Eds.). Handbook
of Statistics, Vol. 16: Order Statistics: Theory and Methods. Balakrishnan, N. and Rao, C. R. (Eds.).
Order Statistics: Applications. Amsterdam, Netherlands: Elsevier, 1998. David,
H. A. Order
Statistics, 2nd ed. Gibbons, J. D.
and Chakraborti, S. (Eds.). Nonparametric
Statistic Inference, 3rd ed. exp. rev. Hogg,
R. V. and Craig, A. T. Introduction
to Mathematical Statistics, 3rd ed. Rose,
C. and Smith, M. D. "Order Statistics." §9.4 in Mathematical
Statistics with Mathematica. Rose, C. and Smith, M. D. "Computational Order Statistics."
Mathematica J. 9 , 790-802, 2005. Referenced on Wolfram|Alpha Order Statistic
Cite this as:
Weisstein, Eric W. "Order Statistic."
From MathWorld https://mathworld.wolfram.com/OrderStatistic.html
Subject classifications
variates 
,
..., 
,
reorder them so that 
.
Then 
is called the 
th
order statistic (Hogg and Craig 1970, p. 146), sometimes also denoted 
. Special cases include the minimum
has probability density function 
and distribution
function 
,
then the probability function of 
is given by
![f_(Y_r)=(N!)/((r-1)!(N-r)!)[F(x)]^(r-1)[1-F(x)]^(N-r)f(x)](/images/equations/OrderStatistic/NumberedEquation6.svg)
,
..., 
(Rose and Smith 2002, pp. 311 and 454).
