Order statistic

Common card · No. 329048

In statistics, the kth order statistic of a statistical sample is equal to its kth-smallest value. Given a sample of size n {\displaystyle n} , the kth order statistic is denoted x ( k ) {\displaystyle x_{(k)}} , with 1 ≤ k ≤ n {\displaystyle 1\leq k\leq n} . Together with rank statistics, order statistics are among the most fundamental tools in non-parametric statistics and 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 sample quantiles. When using probability theory to analyze order statistics of random samples from a continuous distribution, the cumulative distribution function is used to reduce the analysis to the case...

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