Order Statistic

Given a sample of $n$ variates $X_1$, ..., $X_n$, reorder them so that $X'_1<X'_2<\ldots<X'_n$. Then the $i$th order statistic $X^{\left\langle{i}\right\rangle{}}$ is defined as $X'_i$, with the special cases

$$m_n = X^{\left\langle{1}\right\rangle{}}=\min_j(X_j)$$

$$M_n = X^{\left\langle{n}\right\rangle{}}=\max_j(X_j).$$

A Robust Estimation technique based on linear combinations of order statistics is called an L-Estimate.

See also Extreme Value Distribution, Hinge, Maximum, Minimum, Mode, Ordinal Number

References

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

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: Marcel Dekker, 1992.