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تسجيل

Order Statistic

المؤلف:  Balakrishnan, N. and Chen, W. W. S.

المصدر:  Handbook of Tables for Order Statistics from Lognormal Distributions with Applications. Amsterdam, Netherlands: Kluwer, 1999.

الجزء والصفحة:  ...

4-3-2021

5000

Order Statistic

Given a sample of  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

(1)

and maximum

(2)

Important functions of order statistics include the statistical range

(3)

midrange

(4)

and statistical median

{Y_((N+1)/2) if N is odd; 1/2(Y_(N/2)+Y_(1+N/2)) if N is even " src="https://mathworld.wolfram.com/images/equations/OrderStatistic/NumberedEquation5.gif" style="height:50px; width:210px" />

(5)

(Hogg and Craig 1970, p. 152).

If  has probability density function  and distribution function , then the probability function of  is given by

(6)

for , ...,  (Rose and Smith 2002, pp. 311 and 454).

A robust estimation technique based on linear combinations of order statistics is called an L-estimate.

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REFERENCES:

Balakrishnan, N. and Chen, W. W. S. Handbook of Tables for Order Statistics from Lognormal Distributions with Applications. Amsterdam, Netherlands: Kluwer, 1999.

Balakrishnan, N. and Cohen, A. C. Order Statistics and Inference. New York: Academic Press, 1991.

Balakrishnan, N. and Rao, C. R. (Eds.). Handbook of Statistics, Vol. 16: Order Statistics: Theory and Methods. Amsterdam, Netherlands: Elsevier, 1998.

Balakrishnan, N. and Rao, C. R. (Eds.). Order Statistics: Applications. Amsterdam, Netherlands: Elsevier, 1998.

David, H. A. Order Statistics, 2nd ed. New York: Wiley, 1981.

Gibbons, J. D. and Chakraborti, S. (Eds.). Nonparametric Statistic Inference, 3rd ed. exp. rev. New York: Dekker, 1992.

Hogg, R. V. and Craig, A. T. Introduction to Mathematical Statistics, 3rd ed. New York: Macmillan, 1970.

Rose, C. and Smith, M. D. "Order Statistics." §9.4 in Mathematical Statistics with Mathematica. New York: Springer-Verlag, pp. 311-322, 2002.

Rose, C. and Smith, M. D. "Computational Order Statistics." Mathematica J. 9, 790-802, 2005.