Editing Order statistic (section)

{{Short description|Kth smallest value in a statistical sample}}{{more footnotes needed|date=December 2010}}[[File:Order Statistics Exponential PDF.svg|thumb|[[Probability density function]]s of the order statistics for a sample of size ''n''&nbsp;=&nbsp;5 from an [[exponential distribution]] with unit scale parameter]]

In [[statistics]], the ''k''th '''order statistic''' of a [[statistical sample]] is equal to its ''k''th-smallest value.<ref name=david>{{Cite book | last1 = David | first1 = H. A. | last2 = Nagaraja | first2 = H. N. | doi = 10.1002/0471722162 | title = Order Statistics | series = Wiley Series in Probability and Statistics | year = 2003 | isbn = 9780471722168 }}</ref> Together with [[Ranking (statistics)|rank statistics]], order statistics are among the most fundamental tools in [[non-parametric statistics]] and [[non-parametric inference|inference]].

Important special cases of the order statistics are the [[minimum]] and [[maximum]] value of a sample, and (with some qualifications discussed below) the [[sample median]] and other [[quantile|sample quantiles]].

When using [[probability theory]] to analyze order statistics of [[random sample]]s from a [[continuous probability distribution|continuous distribution]], the [[cumulative distribution function]] is used to reduce the analysis to the case of order statistics of the [[uniform distribution (continuous)|uniform distribution]].