Order statistic

Probability density functions of the order statistics for a sample of size n = 5 from an exponential distribution with unit scale parameter

In statistics, the kth order statistic of a statistical sample is equal to its kth-smallest value.[1] 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 of order statistics of the uniform distribution.

  1. ^ David, H. A.; Nagaraja, H. N. (2003). Order Statistics. Wiley Series in Probability and Statistics. doi:10.1002/0471722162. ISBN 9780471722168.